Practice Writing Equations from Context in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

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Quick Recap

Translating real-world situations and word problems into algebraic equations by identifying the unknown, choosing a variable, and expressing relationships mathematically.

Word problems are stories in disguise. Your job is to find the main character (the unknown—call it x), figure out what's happening to it (the operations), and write down the punchline (the equation). 'Five more than twice a number is 17' becomes 2x+5=17.

Showing a random 20 of 50 problems.

Example 1

easy
A number divided by 6 equals 5. Write the equation using y.

Example 2

medium
Maya is 6 years older than her sister Lina. In 4 years, their ages will sum to 30. Let Lina's current age be ℓ; write an equation in ℓ.

Example 3

easy
A number decreased by 8 equals 5. Write an equation using x.

Example 4

easy
Write an equation: 'Three times a number decreased by 4 is 17.'

Example 5

challenge
A ball is thrown upward from a 5-m roof with initial velocity 10 m/s. Its height in meters after t seconds is h(t)=5+10t−5t2. Write the equation for when the ball hits the ground.

Example 6

easy
A number increased by 7 equals 12. Write an equation using x for the number.

Example 7

easy
Four times a number is 36. Write an equation using n.

Example 8

medium
A gym membership has a $30 start-up fee and costs $25/month. The total spent is $255. Write and solve an equation for the number of months m.

Example 9

medium
The length of a rectangle is 3 more than its width w. Its perimeter is 26. Write an equation in w.

Example 10

hard
A rectangle's length is 3 more than its width w. Its area is 108 cm². Write an equation in w and state why it is not linear.

Example 11

easy
Seven more than a number is 20. Write an equation using x.

Example 12

easy
Maria has x dollars. She earns $15 more. Now she has $40. Write the equation.

Example 13

easy
A taxi charges $3 to start and $2 per km. Let d be distance in km and C be total cost. Write the equation for C in terms of d.

Example 14

medium
A jar has nickels and dimes. There are 3 more dimes than nickels, and 12 coins total. Let nickels be n; write the count equation.

Example 15

medium
Admission is $8 for adults and $5 for children. A group of 6 people pays $39. Let adults be a; write the cost equation (children =6−a).

Example 16

medium
A rectangle's length is twice its width w, and its perimeter is 30. Write an equation in w.

Example 17

hard
A worker earns $15/h for the first 40 hours and $22.50/h for overtime. He earned $735 working h hours, where h>40. Write an equation in h.

Example 18

medium
The sum of two consecutive integers is −13. Let the smaller be n; write the equation.

Example 19

easy
A number divided by 3 equals 7. Write the equation using x.

Example 20

medium
A rectangle's length is 4 more than its width w. The perimeter is 40. Write an equation in w.
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