Question

Kim and Sam were each given the same pair of numbers. Sam's description of the two numbers was: The larger number is 3 more than three times the smaller number, . Kim's description of the two numbers was: Five times the smaller number decreased by 7 is the larger number. Which equation represents the situation?

Answer 1

Sam's description =
`3x+3`, Kim's description =
`5x-7`

Explanation:

Given:

Kim and Sam were each given the same pair of numbers.

Sam's description of the two numbers was:

The larger number is 3 more than three times the smaller number.

Kim's description of the two numbers was:

Five times the smaller number decreased by 7 is the larger number.

Question asked:

Which equation represents the situation?

Solution:

Let smaller number =
`x`

According to Sam's description of the two numbers, the equation will be:-

Larger number = 3 more than three times the smaller number

=
`3x+3\ (eq1)`

According to Kim's description of the two numbers was, the equation will be:-

Larger number = Five times decreased by 7

=
`5x-7\ (eq2)`

By equating both equation:-

`5x-7=3x+3\\ \\ Subtracting\ both\ sides\ by \ 3x\\ \\ 5x-3x-7=3x-3x+3\\ \\ 2x-7=3\\ \\ Adding\ both\ sides\ by\ 7\\ \\ 2x-7+7=3+7\\ \\ 2x=10\\ \\ Dividing\ both\ sides\ by\ 2\\ \\ x=5`

Smaller number =
`x` = 5

Larger number =
`3*5+3=15+3=18`

Therefore, equations represents the situation are
`3x+3` and
`5x-7`