Practice Algebraic Representation in Math

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

Quick Recap

Using algebraic expressions and equations to represent and analyze mathematical relationships and real-world situations.

Translating 'the cost is $5 plus $2 per item' into C=5+2nC = 5 + 2n.

Showing a random 20 of 50 problems.

Example 1

easy
Write '3 times a number nn' algebraically.

Example 2

easy
Write an expression for the total cost of nn books at $8 each.

Example 3

easy
Represent this situation algebraically: 'Sarah has 5 more apples than Tom. Together they have 23 apples.'

Example 4

medium
A number nn is multiplied by 3 then 4 is subtracted. The result equals 17. Write the equation and solve.

Example 5

hard
A worker plants pp trees on day 1, then 4 more trees each subsequent day. Write the total planted after dd days.

Example 6

easy
Write an expression for '6 less than a number nn'.

Example 7

challenge
A two-digit number has tens digit tt and units digit uu. Write its value, and the value when the digits are reversed.

Example 8

easy
Write 'the quotient of aa and bb' algebraically.

Example 9

easy
A square has side ss. Write its area and perimeter.

Example 10

medium
A taxi charges $3 base fare plus $2 per mile. Write a formula for the fare FF in terms of miles mm.

Example 11

medium
Translate 'the sum of a number and twice another equals 12' into an equation (numbers a,ba,b).

Example 12

easy
Write an expression for the total length of kk ribbons that are each 4 feet long.

Example 13

medium
Write an algebraic formula for the perimeter of a rectangle with length โ„“\ell and width ww.

Example 14

easy
Write '5 more than a number nn' as an expression.

Example 15

easy
Write 'the sum of xx and yy' as an expression.

Example 16

hard
Three consecutive integers sum to 84. Represent them and solve.

Example 17

medium
Anna has $30. She spends $x\$x on a book and $5 on a sandwich. Write the amount left.

Example 18

medium
Translate 'the product of a number and 4 is 5 less than the number' into an equation (number nn).

Example 19

medium
A rectangle's length is 3 more than its width ww. Write its perimeter.

Example 20

hard
A movie ticket costs $aa for adults and $cc for children. A family of 2 adults and 3 children pays $54. Write the equation; if a=12a = 12, find cc.