Question

Twice a number added to a smaller number is 5. The difference of 5 times the smaller number and the larger number is 3. Let x represent the smaller number and y represent the larger number. Which equations represent the situation?

Answer 1

$\begin{gathered}\begin{gathered}\bf Let - \begin{cases} &\sf{x \: represent \: the \: smaller \: number} \\ &\sf{y \: represent \: the \: larger \: number} \end{cases}\end{gathered}\end{gathered}$

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$\begin{gathered}\begin{gathered}\bf Given - \begin{cases} &\sf{Twice \: a \: larger \: number \: added \: to \: smaller \: number \: is \: 5.} \\ &\sf{The \: difference \: of \: 5 \: times \: the \: smaller \: number \: and \: the \: larger \: number \: is \: 3.} \end{cases}\end{gathered}\end{gathered}$

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$\begin{gathered}\begin{gathered}\bf So, \: equations \: are \begin{cases} &\sf{2y + x = 5} \\ &\sf{5x - y = 3} \end{cases}\end{gathered}\end{gathered}$

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Answer 2

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Let the numbers be "x" and "y"

2y + x = 5

5x - y = 3

y = 5x - 3

2(5x - 3) + x = 5

10x - 6 + x = 5

11x = 11

x = 1

Substituting x=1 in y = 5x - 3

y = 5(1) - 3

y = 2