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The larger of two numbers is 10 more than 3 times the smaller number. The difference between the two numbers is 28. What is the sum of the two numbers?

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Let:

• x ,be the large number

,

• y, be the small number

"The larger of two numbers is 10 more than 3 times the smaller number"

means:


x=3y+10

And

"The difference between the two numbers is 28"

means:


x-y=28

Notice that we get the following system of equations:


\begin{cases}x=3y+10 \\ x-y=28\end{cases}

Now, let's subtitute equation 1 into equation 2 and solve for y :


\begin{gathered} x-y=28 \\ \rightarrow3y+10-y=28 \\ \rightarrow2y=18\rightarrow y=(18)/(2) \\ \rightarrow y=9 \end{gathered}

Now, substituting in equation 1 and solving for x :


\begin{gathered} x=3y+10 \\ \rightarrow x=3(9)+10 \\ \rightarrow x=37 \end{gathered}

This way, we can conclide that both numbers are 37 and 9, and that their sum


x+y\rightarrow37+9\rightarrow46

is 46

User Ddayan
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