Answer:
Sam's description =
, Kim's description =
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?
<u>Solution:</u>
Let smaller number = ![x](https://tex.z-dn.net/?f=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)](https://tex.z-dn.net/?f=3x%2B3%5C%20%28eq1%29)
According to Kim's description of the two numbers was, the equation will be:-
Larger number = Five times decreased by 7
= ![5x-7\ (eq2)](https://tex.z-dn.net/?f=5x-7%5C%20%28eq2%29)
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](https://tex.z-dn.net/?f=5x-7%3D3x%2B3%5C%5C%20%5C%5C%20Subtracting%5C%20both%5C%20sides%5C%20by%20%5C%203x%5C%5C%20%5C%5C%205x-3x-7%3D3x-3x%2B3%5C%5C%20%5C%5C%202x-7%3D3%5C%5C%20%5C%5C%20Adding%5C%20both%5C%20sides%5C%20by%5C%207%5C%5C%20%5C%5C%202x-7%2B7%3D3%2B7%5C%5C%20%5C%5C%202x%3D10%5C%5C%20%5C%5C%20Dividing%5C%20both%5C%20sides%5C%20by%5C%202%5C%5C%20%20%5C%5C%20x%3D5)
Smaller number =
= 5
Larger number = ![3\times5+3=15+3=18](https://tex.z-dn.net/?f=3%5Ctimes5%2B3%3D15%2B3%3D18)
Therefore, equations represents the situation are
and