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A store buys 15 sweaters for $90 and sells them for $405. If p represents the total profit in dollars and cents when the store buys any number of sweaters, s, write a proportional equation for p in terms of
s that matches the context.
p=_____

A store buys $15$ sweaters for $\$ 90$ and sells them for $\$ 405$ . If $p$ represents the total profit in dollars and cents when the store buys any number of sweaters, $s$ , write a proportional equation for $p$ in terms of $s$ that matches the context. $\newline$ $p=\_\_\_\_\_$

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Evaluate two-variable equations: word problems

Full solution

Q. A store buys

15

sweaters for

\$ 90

and sells them for

\$ 405

. If

p

represents the total profit in dollars and cents when the store buys any number of sweaters,

s

, write a proportional equation for

p

in terms of

s

that matches the context.

\newline

p=\_\_\_\_\_

Calculate profit per sweater: Determine the profit per sweater. The store buys $15$ sweaters for $\$90$ and sells them for $\$405$ . To find the profit per sweater, we first need to calculate the total profit made from selling all $15$ sweaters. Total profit = Selling price - Buying price Total profit = $\$405 - \$90$
Calculate total profit: Calculate the total profit. $\newline$ Now we perform the subtraction to find the total profit. $\newline$ Total profit = $\$405 - \$90$ $\newline$ Total profit = $\$315$
Find profit per sweater: Find the profit per sweater. $\newline$ To find the profit per sweater, we divide the total profit by the number of sweaters. $\newline$ Profit per sweater = Total profit / Number of sweaters $\newline$ Profit per sweater = $\$315 / 15$
Calculate profit per sweater: Calculate the profit per sweater. $\newline$ Now we perform the division to find the profit per sweater. $\newline$ Profit per sweater = $\$315 / 15$ $\newline$ Profit per sweater = $\$21$
Write proportional equation: Write the proportional equation. $\newline$ Since the profit is directly proportional to the number of sweaters, we can write the equation for the total profit $p$ in terms of the number of sweaters $s$ as follows: $\newline$ $p = \text{Profit per sweater} \times s$ $\newline$ $p = \$(21) \times s$

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