What is the cost per foot of redwood and of pine.

Question

A carpenter purchased 50 ft of redwood and 70 ft of pine for a total cost of $253. A second purchase, at the same prices, included 100 ft of redwood and 60 ft of pine for a total cost of $394. Find the cost per foot of redwood and of pine.

Answer 1

Hi Chloe,

introducing the variables r = redwood price per foot and p = pine price per foot

we have the equations 50r + 70p = 253 (equation 1)

and 100r + 60p = 394 (equation 2)

multiplying equation 1 by -2 -100r - 140p = -506 (equation 3)

if you add equation 2 and equation 3, you will eliminate the variable r

100r + 60p - 100r -140p = 394 - 506

-80p = -112

divide both sides by -80, you get the pine price per foot p = -112/-80 = $1.40

substitute this price into equation 1 and we get 50r + 70($1.40) = $253

50r + 98 = 253

50r = 253 - 98

50 r = 155

r = 155/50 = $3.10

verify your solution in equation 2: 100r + 60p = 394

100 ($3.10) + 60($1.40) = 394

$310 + $84 = $394

$394 = $394