Question 92979
{{{x+y=112}}} "The sum of two numbers is 112."

{{{y=4x+7}}} "The second is 7 more than 4 times the first."


{{{x+(4x+7)=112}}} Plug in {{{y=4x+7}}}



{{{5x+7=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=(105)/(5)}}} 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+7}}}  to find y


{{{y=4(21)+7}}}


{{{y=84+7}}}


{{{y=91}}}



So the two numbers are 21 and 91


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Check:


{{{21+91=112}}} plug in x=21, y=91


{{{112=112}}} works