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 xx), 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=172x + 5 = 17.

Showing a random 20 of 50 problems.

Example 1

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

Example 2

medium
Maya is 66 years older than her sister Lina. In 44 years, their ages will sum to 3030. Let Lina's current age be ℓ\ell; write an equation in ℓ\ell.

Example 3

easy
A number decreased by 88 equals 55. Write an equation using xx.

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 55-m roof with initial velocity 1010 m/s. Its height in meters after tt seconds is h(t)=5+10t−5t2h(t)=5+10t-5t^2. Write the equation for when the ball hits the ground.

Example 6

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

Example 7

easy
Four times a number is 3636. Write an equation using nn.

Example 8

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

Example 9

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

Example 10

hard
A rectangle's length is 33 more than its width ww. Its area is 108108 cm². Write an equation in ww and state why it is not linear.

Example 11

easy
Seven more than a number is 2020. Write an equation using xx.

Example 12

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

Example 13

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

Example 14

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

Example 15

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

Example 16

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

Example 17

hard
A worker earns $15\$15/h for the first 4040 hours and $22.50\$22.50/h for overtime. He earned $735\$735 working hh hours, where h>40h>40. Write an equation in hh.

Example 18

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

Example 19

easy
A number divided by 33 equals 77. Write the equation using xx.

Example 20

medium
A rectangle's length is 44 more than its width ww. The perimeter is 4040. Write an equation in ww.
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