SOLUTION: A carpenter purchased 70 ft of redwood and 80 ft of pine for a total cost of $335. A second purchase, at the same prices, included 100 ft of redwood and 50 ft of pine for a total c

Question 1169905: A carpenter purchased 70 ft of redwood and 80 ft of pine for a total cost of $335. A second purchase, at the same prices, included 100 ft of redwood and 50 ft of pine for a total cost of $395. Find the cost per foot of redwood and of pine.
Found 3 solutions by ikleyn, MathTherapy, greenestamps:
Answer by ikleyn(52814)   (Show Source): You can put this solution on YOUR website!
.

Let x = price per 1 ft of redwood; y = price for 1 ft of pine. Then you have the system of these 2 equations in 2 unknowns 70x + 80y = 335 (1) 100x + 50y = 395 (2) Appliy any method you want (you know, you like). I will use the determinant method (= same as the Cramer's rule) x = = 3.30 dollars per foot y = = 1.30 dollars per foot.

Solved.

Answer by MathTherapy(10555)   (Show Source): You can put this solution on YOUR website!

A carpenter purchased 70 ft of redwood and 80 ft of pine for a total cost of $335. A second purchase, at the same prices, included 100 ft of redwood and 50 ft of pine for a total cost of $395. Find the cost per foot of redwood and of pine.

Let cost of each foot of redwood and pine, be R and P, respectively
We then get: 70R + 80P = 335______14R + 16P = 67 ------- eq (i)
100R + 50P = 395_____20R + 10P = 79 ------- eq (ii)
6R - 6P = 12 ------ Subtracting eq (i) from eq (ii)
6(R - P) = 6(2)______R - P = 2________R = 2 + P ------- eq (iii)
14(2 + P) + 16P = 67 ------- Substituting 2 + P for R in eq (i)
28 + 14P + 16P = 67
30P = 39
Cost of each foot of pine, or
R = 2 + 1.30 ------- Substituting 1.30 for P in eq (iii)
Cost of each foot of redwood:
Answer by greenestamps(13203)   (Show Source): You can put this solution on YOUR website!

The given information gives us two equations:

My definite preference for solving a system of equations in this form is elimination. Multiply one or both equations by constants so that the coefficients of one of the variables are the same in the two equations; then subtract one equation from the other to eliminate that variable.

Then substitute x=3.3 in either original equation to solve for y.

ANSWERS: x = $3.30 per foot for redwood; y = $1.30 per foot for pine.

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