Algebra word problem

Question

Katherine and Corey collect stamps. Corey collected 23 fewer than 5 times the number of Katherine’s stamps. Altogether, they collected 1129 stamps. How many stamps did each person collect? Write an equation that models this situation, solve the equation, and answer the question using complete sentences.

Answer 1

Katherine and Corey are collecting stamps. You start by assigning values:

Katherine: x stamps

Corey: 5x - 23 stamps, where the 5x represents 5 times Katherine's stamps, and the - 23 represents 23 fewer

The two together collect 1129 stamps, so you can setup the equation:

x + (5x -23) = 1129 an equation which models this situation

x + 5x - 23 = 1129 equation written without parentheses

6x - 23 = 1129 combining like terms

+23 +23 addition property of equality, to get variables on one side, numbers on the other

6x 1152

6 6 division property of equality, to solve for x (divide by the coefficient of x)

x = 192 stamps, and by substitution, 5x - 23 = 5(192) - 23 = 937 stamps

Written as a complete sentence:

Katherine collects 192 stamps and Corey collects 937 stamps, for a total of 1129 stamps.

Answer 2

Let's take the number of stamps Katherine collected as x.

Therefore, the number of stamps Corey collected can be represented as 5x−23

x+(5x-23)=1129

6x=1129+23

6x=1152

x=192

5x-23=5*192-23=937

Therefore, Katherine collected 192 and Corey collected 937 stamps.