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There is a number that is three-fifths the total of the other number. When four is added to one of the numbers, their sum will be equal to the other number. There are two pairs of numbers that satisfy these descriptions. What are they?

Correct answer:

a =  7.5
b =  12.5

Step-by-step explanation:

$$\begin{gathered} a=\frac{3}{5}\cdot b \\ a+5=b \\ a=3/5\cdot b \\ a+5=b \\ 5a-3b=0 \\ a-b=-5 \\ Row2-\frac{1}{5}\cdot Row1\to Row2 \\ 5a-3b=0 \\ -0.4b=-5 \\ b=\frac{-5}{-0.4}=12.5 \\ a=\frac{0+3b}{5}=\frac{0+3\cdot 12.5}{5}=7.5 \\ a=\frac{15}{2}=7.5 \\ b=\frac{25}{2}=12.5 \end{gathered}$$

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