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

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 .

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