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Tom can save $25$ dollars in $4$ days. Sally can save $48$ dollars in $6$ days. How many days will it take Sally to save $100$ dollars more than Tom.

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Solve proportions: word problems

Full solution

Q. Tom can save

25

dollars in

4

days. Sally can save

48

dollars in

6

days. How many days will it take Sally to save

100

dollars more than Tom.

Calculate Tom's rate: Calculate Tom's daily saving rate. $\newline$ Tom's rate = $\frac{25 \text{ dollars}}{4 \text{ days}} = 6.25 \text{ dollars/day}.$
Calculate Sally's rate: Calculate Sally's daily saving rate. $\newline$ Sally's rate = $\frac{48 \text{ dollars}}{6 \text{ days}} = 8 \text{ dollars/day}.$
Set up equation: Set up the equation to find the number of days $d$ it takes for Sally to save $100$ dollars more than Tom. $\newline$ Sally's total = Sally's rate $* d$ $\newline$ Tom's total = Tom's rate $* d$ $\newline$ Sally's total = Tom's total $+ 100$ $\newline$ $8d = 6.25d + 100$
Solve for d: Solve for d. $\newline$ $8d - 6.25d = 100$ $\newline$ $1.75d = 100$ $\newline$ $d = \frac{100}{1.75}$ $\newline$ $d = 57.14$ days

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