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

Answer:

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

Step-by-step 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 = $3\times5+3=15+3=18$

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