Systems from word problems
Systems from word problems
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Total answers
Read the problem and find the two numbers.
The sum of two numbers is 11 and their difference is 5. Find the two numbers.
What does the generator do?
It makes a word problem giving the sum and difference of two whole numbers and asks for the numbers.
How to solve
Write x + y = sum and x − y = difference. Adding them gives 2x = sum + difference, so x is half of that; then y = sum − x.
Other exercise generators:
- Absolute value and the opposite number
- Compare absolute values
- Add and subtract integers
- Adding with Images
- Addition and Subtraction Exercises
- Addition within 100 — no regrouping
- Addition within 100 — with regrouping
- Addition & subtraction within 20
- Angle from a circle
- Classify the angle
- Classify an angle by its measure
- Measure an angle with a protractor
- Measure an angle with a protractor
- Angle sum in a quadrilateral
- Angle sum in a triangle
- Vertical and supplementary angles
- Alternate angles on parallel lines
- Corresponding angles on parallel lines
- Area by counting squares
- Identify the association
- Axes of symmetry of a shape
- Read a bar chart
- Bar charts (advanced)
- Second binomial formula — expand (ax − b)²
- Recognize the binomial formula
- Third binomial formula — (ax − b)(ax + b)
- First binomial formula — expand (ax + b)²
- Compare two box plots
- Pick the correct box plot for the data
- Read values off a box plot
- Building Blocks
- Point symmetry — find the image of a point
- Area of a circle from the radius
- Word problem — area of a circle
- Circumference of a circle from the radius
- Find the radius from the circumference
- Classify the quadrilateral
- Classify a triangle by its angles
- Column addition — two-digit
- Column addition — 3 digits
- Column addition — 4-digit numbers
- Column subtraction — 3 digits
- Column subtraction — 4-digit numbers
- Compare the number of balls
- Compare two line graphs
- Compare integers
- Comparing Numbers
- Comparing within 100
- Compare numbers to 1,000
- Compare numbers up to 10,000
- Comparing within 20
- Compare large numbers
- Comparing Powers
- Compare scientific notation
- Complete the symmetric figure
- Perimeter and area of composite figures
- Cone Surface Area
- Cone Volume
- Count back through zero
- Combinations — tree diagram
- Counting Tens
- Counting tens
- Counting
- Cross Out
- Building from plan
- Cube buildings – mixed
- Total number of cubes
- Count visible cubes
- Cube net
- Cube root (perfect cube)
- Surface area of a cube
- Building views
- Surface area of a cuboid
- Cuboid surface from net
- Cuboid surface area with decimal edges
- Volume by counting unit cubes
- Volume of a cuboid (formula)
- Volume of a cuboid with fractional edges
- Cylinder Surface Area
- Cylinder Volume
- Add and subtract decimals
- Compare decimals
- Divide a decimal by a decimal
- Divide a decimal by a whole number
- Decimals and fractions
- Multiply and divide decimals by 10, 100, 1000
- Multiply a decimal by a whole number
- Decimal on a number line
- Decimal place value
- Recurring or terminating decimal?
- Round decimals
- Decompose Powers into Product
- Digit at a given place
- Which digit is in the …?
- Distance between two points on a gridline
- Divide by 10, 100, 1000
- Long division
- Long division by a two-digit number
- Long division with remainder
- Divisibility rules
- Dividing by 2, 5, 10
- Division as sharing
- Fact families
- Reading dot plots
- Read a double bar graph
- Draw a polygon from coordinates
- Equation Solver
- Distributive property – equivalent expressions
- Evaluate an expression
- Evaluating expressions
- Evaluate an expression with two variables
- Evaluate a root expression
- Expand using the distributive property
- Expanded form
- Expanded form (up to 10,000)
- Expanded form (up to a million)
- Combining Like Terms
- Equivalent Expressions
- Evaluating Expressions
- Expanding Parentheses
- Factoring Out
- Algebraic Fractions
- Multiplying by a Monomial
- Cube of a Binomial
- Multiplying Binomials
- Substitution into Expressions
- Factor out a common factor
- All factors of a number
- Find the Correct Exercise
- Find the missing number to 1,000
- Find the Bigger or Smaller Number
- Integer expressions (order of operations)
- Fraction, decimal and percent — the same thing in three forms
- Divide a fraction by a fraction
- Fractions — multi-step expressions
- Name the fraction
- Fraction of a set
- Fraction of a set
- Write the fraction
- Shade the fraction
- Add fractions with different denominators
- Add fractions (same denominator)
- Compare fractions
- Equivalent fractions
- Multiply a fraction by a whole number
- Fraction of a number
- Subtract fractions with different denominators
- Subtract fractions (same denominator)
- Direct Proportion
- Domain of a Function
- Inverse Proportion
- Linear Function
- Range of a Function
- Reading from Graph
- Function Table
- Dependent and Independent Variables
- Greatest common factor (GCF)
- Reading histograms
- Find a number up to 100
- Linear Inequalities - Basic
- Inequalities - Variable on Both Sides
- Inequalities - Intervals
- Inequalities - Mixed Problems
- Inequalities - Number Line
- Inequalities - Special Cases
- Inequalities with Fractions
- Inequalities with Parentheses
- Do we need brackets?
- Inverse rule of three
- Least common multiple (LCM)
- Compare lengths in different units
- Compare lengths
- Compare lengths in mixed units
- Compare lengths
- Convert from a larger unit to a smaller one
- Length: convert down
- Convert from a smaller unit to a larger one
- Length: convert up
- Fill in the unit
- Length: fill the missing unit
- Compare imperial units
- Imperial length: compare
- Imperial units – larger to smaller
- Imperial length: convert down
- Imperial units – smaller to larger
- Imperial length: convert up
- Arithmetic with mixed units
- Convert two units to one
- Length units
- Length units — cm and m
- Line of best fit
- Line plot with fractions
- Word problem with a linear equation
- Linear Equations - Basic
- Linear Equations - Both Sides
- Unknown in Denominator on Both Sides
- Unknown on Both Sides with Fractions
- Equivalent Equations
- Equations with Fractions - Unknown in Denominator
- Equations with Fractions - Unknown in Numerator
- Linear Equations - Number of Solutions
- Equations with Plus on One Side
- Equations with Two Plus Terms
- One-step linear inequality
- Arrangements — systematic listing
- Loan — monthly instalment
- Mean (Average)
- Comparing measurements
- Median
- Mixed number ↔ improper fraction
- Mixed and improper fractions
- Mode
- Coin combinations
- Combine coins
- Count the money
- Count money
- Euros and cents — decimal notation
- Making change
- Make change
- Money word problems
- Money word problems
- Multiples of a number
- Multiplication and Division Exercises
- Times tables 2, 5, 10
- Multiplication as an array
- Multiplication as an array — review
- Multiplication as addition
- Times tables — quick drill
- Find the missing factor
- Fill the missing times-table cell
- Times tables 1 to 12
- Multiplication word problems
- Times-tables word problems
- 2-digit × 2-digit multiplication
- Multiply and divide by 10, 100, 1000
- Column multiplication up to 10,000
- Multi-digit × 1-digit multiplication
- Long multiplication with multi-digit numbers
- Multiply and divide integers
- Multiplying a round number by a one-digit number
- Multiplying a round number by the same digit
- Negative number on a number line
- Number Line
- Number Line up to 10
- Number on a 0–100 line
- Number line to 1,000
- Number Chain
- Addition Pyramid
- Number Series Completion
- One-step equations – add and subtract
- One-step equations – multiply and divide
- Multiply in scientific notation
- Order Numbers
- Order numbers to 100
- Order numbers to 1,000
- Order Numbers up to 10,000
- Order of operations — with brackets
- Find the right expression
- Order of operations — no brackets
- Multi-step problems — order of operations
- Choosing pairs
- Parallel, perpendicular or intersecting?
- Area of a parallelogram
- Perimeter of a parallelogram
- Percent change (increase / decrease)
- Percent error of a measurement
- Find the whole from a part and a percent
- Read the percentage from a 100-grid
- Percent of an amount — discount, tax, tip
- Percent of a whole number
- Percentage word problem
- Perimeter — square and rectangle
- Triangle perimeter
- Perimeter of a triangle
- Read a pictograph
- Reading pie charts
- Place of a digit
- What place is the digit in?
- Hundreds, tens and ones
- Tens and ones
- Perimeter and area – mixed problems
- Plot a point on the coordinate grid
- Plot a point — all four quadrants
- Addition and subtraction to 1,000
- Addition and Subtraction with Numbers Up to 10,000
- Addition and Subtraction Patterns up to 10,000
- Point symmetry — find the centre
- Interior angle sum of a polygon
- Classify polygons
- Classify quadrilaterals
- Sides and vertices
- Direction and turns
- Power laws (same base)
- Powers
- Powers Calculation
- Powers and decimal places
- Powers Simplification
- Powers with Fractions
- Powers with Letters
- Powers with Unknown Exponent
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- exercises.prima-07-circles-in-circle.title
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- exercises.prima-14-strike-out-digits.title
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- Prime factorisation
- Prime or composite?
- Volume of a prism — from base area and height
- Compound event — coin and die
- Experimental vs theoretical probability
- Probability of a simple event
- Per mille (‰) — introduction
- Read from a proportion graph
- Rule of three — direct proportion
- Pyramid Surface Area
- Pyramid Volume
- Pythagorean theorem — find the hypotenuse
- Pythagorean theorem — find a leg
- Pythagorean Theorem – Find the Hypotenuse
- Pythagorean Theorem – Find a Leg
- Pythagorean Theorem – Mixed Practice
- Verify a Right Triangle
- Pythagorean Theorem – Word Problems
- Word problem — ladder against a wall
- Name the quadrilateral
- Quartiles — compute Q1, median and Q3
- Random sample — estimating the population
- Range
- Equivalent ratio — fill in the missing term
- Ratio in simplest form
- Rational or irrational?
- Read coordinates of a point
- Read coordinates — all four quadrants
- Read a line graph
- Reading a ruler
- Recipe — how much of each ingredient?
- Reflect a point
- Right angles
- Right, acute and obtuse angles
- Roman numerals — mixed
- Read Roman numerals
- Write Roman numerals
- Rounding large numbers
- Round large numbers
- Round to the nearest 10 and 100
- Round 4-digit numbers
- Sample space — list all outcomes
- Savings — final balance
- Map scale
- Scatter plots — association
- Scientific notation → standard form
- Find the shapes
- Find the shape in the picture
- Name the shape
- Name the shape
- Name the shape
- Operations on signed fractions
- Triangle Similarity – Missing Side
- Triangle Similarity – Mixed Problems
- Triangle Similarity – Similarity Ratio
- Triangle Similarity – Similarity Theorems
- Simple interest
- Simplifying exponents
- Simplify a linear expression
- Skip counting
- Faces, edges, and vertices
- Faces, edges, vertices
- Name the solid
- Objects around us
- Surface Area & Volume - Mixed
- Recognising solids – mixed
- Solve p · (x + q) = r
- Solve px + q = r
- Unknown on both sides
- Sphere Surface Area
- Sphere Volume
- Area of square and rectangle
- Area of squares and rectangles
- Perimeter of square and rectangle
- Perimeter of squares and rectangles
- Estimate a square root
- Square root (perfect square)
- Subtraction within 100 — no borrowing
- Subtraction within 100 — with borrowing
- Line of symmetry
- Line of symmetry
- Lines of symmetry
- Systems by elimination
- Solve a system from a graph
- Systems by substitution
- Read a tally chart
- Tally charts (advanced)
- Temperature word problem
- Tens and ones
- Thales's theorem — construct a right triangle
- Thales's theorem — find the right angle
- Thales's theorem — tangent from a point
- Equations with three members
- Clock — to the minute
- Clock to 5 minutes
- Read the clock — to any minute
- Telling time — full hours
- Clock — whole hours (review)
- Hours and minutes conversion
- Time: convert units
- Days of the week and months
- Elapsed time
- Elapsed time problems
- Area of a trapezoid
- Perimeter of a trapezoid
- Area of triangle
- Triangle congruence criterion
- Perimeter of triangle
- Volume of a triangular prism
- Two-way tables
- Unit rate
- Converting units of volume
- Volume units — ml and l
- Capacity: convert millilitres and litres
- Weight units
- Weight units — g and kg
- Mass: convert grams and kilograms
- Word problems to 1,000
- Word problems — add and subtract to 1000
- Word problems — addition
- Word problems
- Word problems — compare and total
- Comparison word problems
- Word problems with decimals
- Word problems — division
- Division word problems
- Word problems with fractions
- Word problems — multiplication
- Multiplication word problems
- Word problems — two steps
- Multi-step word problems
- Multi-step word problems
- Multi-step word problem
- Multi-step word problems
- Multi-step word problems — mixed
- Word problems with percentages
- Multi-step percent word problems
- Perimeter and area word problem
- Word problems with ratios
- Word problems with ratios — follow-up
- Word problems with rational numbers
- Rule of three — direct and inverse proportion
- Word problems — subtraction
- Word problem with decimals
- Word problem with fractions
- Match the expression to the words
- Writing expressions with a variable
- Write in scientific notation
- Number of trailing zeros