SOLUTION: The sum of two numbers is 112. the second is 7 more than 4 times the first. What are the two numbers?

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Question 92979: The sum of two numbers is 112. the second is 7 more than 4 times the first. What are the two numbers?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
x%2By=112 "The sum of two numbers is 112."
y=4x%2B7 "The second is 7 more than 4 times the first."

x%2B%284x%2B7%29=112 Plug in y=4x%2B7


5x%2B7=112 Combine the variable terms x and 4x on the left side to get 5x



5x=112-7 Subtract 7 from both sides




5+x=105 Combine like terms -7 and 112 on the right side to get 105





x=%28105%29%2F%285%29 Now divide both sides by 5 to isolate and solve for x


x=+21 Reduce



So one answer is
x=+21


Now plug in x=21 into y=4x%2B7 to find y

y=4%2821%29%2B7

y=84%2B7

y=91


So the two numbers are 21 and 91



Check:

21%2B91=112 plug in x=21, y=91

112=112 works