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The larger of two numbers is 33 more than the smaller. When added together, the sum of the larger number and five times the smaller number is 129. What are the two numbers? 

 Jul 23, 2020
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The larger of two numbers is 33 more than the smaller.
When added together, the sum of the larger number and five times the smaller number is 129.
What are the two numbers?

 

\(\text{Let large number $=l$} \\ \text{Let small number $=s$}\)

 

\(\begin{array}{|lrcll|} \hline (1) & l &=& s +33 \\ (2) & l+5s &=& 129 \\ & s+33 + 5s &=& 129 \\ & 6s &=& 129 - 33 \\ & 6s &=& 96 \quad |\quad : 6 \\ & \mathbf{s} &=& \mathbf{16} \\\\ & l &=& s+33\\ & l &=& 16+33 \\ & \mathbf{l} &=& \mathbf{49} \\ \hline \end{array}\)

 

The two numbers are 16 and 49

 

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 Jul 23, 2020

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