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# a carpenter purchase 60 feet of redwood and 80 feet of pine for a total cost of $324 a second purchase at the same price including 90 feet of redwood and 50 feet of pine for a total cost of$381 Find the cost per foot of the redwood in of the pine

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## Answer to a math question a carpenter purchase 60 feet of redwood and 80 feet of pine for a total cost of $324 a second purchase at the same price including 90 feet of redwood and 50 feet of pine for a total cost of$381 Find the cost per foot of the redwood in of the pine

Jett
4.7
1. Let the cost per foot of redwood be r .
2. Let the cost per foot of pine be p .
3. Set up the equations based on the given purchases:
60r + 80p = 324 \quad \text{$1$}
90r + 50p = 381 \quad \text{$2$}
4. Multiply equation $1$ by 3 and equation $2$ by 2 to make the coefficients of r the same:
180r + 240p = 972 \quad \text{$3$}
180r + 100p = 762 \quad \text{$4$}
5. Subtract equation $4$ from equation $3$:
$180r + 240p$ - $180r + 100p$ = 972 - 762
140p = 210
6. Solve for p :
p = \frac{210}{140}
p = 1.50
7. Substitute p = 1.50 into equation $1$:
60r + 80$1.50$ = 324
60r + 120 = 324
60r = 204
r = \frac{204}{60}
r = 3.40
8. Thus, the cost per foot of redwood is \$3.40 and the cost per foot of pine is \$1.50 .

\text{Cost of redwood per foot: } \$3.40 \\\text{Cost of pine per foot: } \$1.50
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