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

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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

2. Let the cost per foot of pine be

3. Set up the equations based on the given purchases:

4. Multiply equation (1) by 3 and equation (2) by 2 to make the coefficients of

5. Subtract equation (4) from equation (3):

6. Solve for

7. Substitute

8. Thus, the cost per foot of redwood is

Answer:

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