Respuesta :
Answer:
Sam's description = [tex]3x+3[/tex], Kim's description = [tex]5x-7[/tex]
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 = [tex]x[/tex]
According to Sam's description of the two numbers, the equation will be:-
Larger number = 3 more than three times the smaller number
= [tex]3x+3\ (eq1)[/tex]
According to Kim's description of the two numbers was, the equation will be:-
Larger number = Five times decreased by 7
= [tex]5x-7\ (eq2)[/tex]
By equating both equation:-
[tex]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[/tex]
Smaller number = [tex]x[/tex] = 5
Larger number = [tex]3\times5+3=15+3=18[/tex]
Therefore, equations represents the situation are [tex]3x+3[/tex] and [tex]5x-7[/tex]
