Application Problem

Question

A carpenter purchased 60 ft of redwood and 90 ft of pine for a total cost of $303. A second purchase, at the same prices, included 90 ft of redwood and 60 ft of pine for a total cost of $357. Find the cost per foot of redwood and of pine.

Answer 1

Let R = cost per foot of redwood, and

let P = cost per foot of pine.

The 1st sentence gives us 60 ft * R + 90 ft * P = $303, and

the 2nd sentence gives us 90 ft * R + 60 ft * P = $357.

So this is two equations and two unknowns, so we should be able to solve these.

Solve the first equation for P: 60 ft * R + 90 ft * P = $303

Subtract 60 ft * R from both sides of the equation: 90 ft * P = $303 - 60 ft * R

Now divide both sides of the equation by 90 ft: P = ($303 - 60 ft * R) / 90 ft = $101 / 30 ft - 2/3 * R

Next, substitute P into the second equation: 90 ft * R + 60 ft * P = $357

so we then have 90 ft * R + 60 ft * [$101 / 30 ft - 2/3 * R] = $357.

Now solve for R (remember, parentheses, exponents, multiplication and division, addition and subtraction):

90 ft * R + [$202 - 40 ft * R] = 50 ft * R + $202 = $357, or 50 ft * R = $155; so R = $155 / 50 ft = $3.10 / ft.

Now we can substitute this value for R into the first equation and solve for P: 60 ft * R + 90 ft * P = $303

so we then have 60 ft * $3.10 / ft + 90 ft * P = $303, or $186 + 90 ft * P = $303.

Subtracting $186 from both sides of the equation, and then dividing by 90 ft, we have P = $1.30 / ft

So P = $1.30/ft, and R = $3.10/ft.

To check this answer, plug both into the second equation:

90 ft * R + 60 ft * P = $357

90 ft * $3.10/ft + 60 ft * $1.30/ft = $279 + $78 = $357, so our answer checks out.

Answer 2

I worked on the problem before seeing it had already been well-answered. I'll simply simply say that using a table is helpful for keeping everything straight. The information is no different than that already provided, but you might see something useful from this perspective. The table may be found here: https://docs.google.com/spreadsheets/d/1AwY5IakIuA8w_HfCrABWa9CDd9CqO_RzMHnfHaK61_k/edit?usp=sharing

Bob

Answer 3

So first define some variables. Let the price per foot of redwood be x and the price per foot of pine be y.

The total cost of redwood is x times the number of feet purchased and the total cost of pine is y times the number of feet purchased. So from the problem the two purchases can be represented algebraically as:

60x + 90y = 303

90x + 60y = 357

All that's left to do is solve these equations for x and y.