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Faisal had $140$ stickers and Adam had $92$ stickers at first. After they each gave away all equal number of stickers, Faisal and $4$ times as many stickers as Adam. How many stickers did each of them give away?

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Solve proportions: word problems

Full solution

Q. Faisal had

140

stickers and Adam had

92

stickers at first. After they each gave away all equal number of stickers, Faisal and

4

times as many stickers as Adam. How many stickers did each of them give away?

Define Variables: Let's define the variables: $\newline$ Let $x$ be the number of stickers each of them gave away. $\newline$ Faisal's remaining stickers = $140 - x$ $\newline$ Adam's remaining stickers = $92 - x$ $\newline$ According to the problem, after giving away the stickers, Faisal has $4$ times as many stickers as Adam. $\newline$ So, we can write the equation: $\newline$ $140 - x = 4(92 - x)$
Solve Equation: Now, let's solve the equation: $\newline$ $140 - x = 4 \times 92 - 4x$ $\newline$ $140 - x = 368 - 4x$ $\newline$ To isolate the variable $x$ , we'll move all terms involving $x$ to one side and constants to the other side: $\newline$ $140 - 368 = -4x + x$ $\newline$ $-228 = -3x$ $\newline$ Now, divide both sides by $-3$ to solve for $x$ : $\newline$ $x = \frac{-228}{-3}$ $\newline$ $x = 76$
Check Solution: We have found that $x$ , the number of stickers each of them gave away, is $76$ . Now let's check if this makes sense with the original numbers: $\newline$ Faisal's remaining stickers = $140 - 76 = 64$ $\newline$ Adam's remaining stickers = $92 - 76 = 16$ $\newline$ According to the problem, Faisal should have $4$ times as many stickers as Adam after they gave away the stickers: $\newline$ $64 = 4 \times 16$ $\newline$ $64 = 64$ $\newline$ This is true, so our solution is correct.

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