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The sum of two numbers is 60. The larger number is 6 more than the smaller number. What are the numbers.Larger number:Smaller numbers:

User Rebooting
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Let the smaller number be 'x' and the larger number be 'y'.

Given that the sum of the numbers is 60,


\begin{gathered} x+y=60 \\ y=60-x \end{gathered}

Also, given that the larger number is 6 more than the smaller number,


y=x+6

Substitute the value,


x+6=60-x

Taking the variables and constants on either side,


\begin{gathered} x+x=60-6 \\ 2x=54 \end{gathered}

Divide both sides by 2,


\begin{gathered} (2x)/(2)=(54)/(2) \\ x=27 \end{gathered}

Substitute this value and obtain the other variable,


\begin{gathered} y=60-27 \\ y=33 \end{gathered}

Thus, the larger number is 33 and the smaller number is 27.

User Alec Rooney
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