Question

A carpenter purchased 50 ft of redwood and 80 ft of pine for a total cost of $285. A second purchase, at the same prices, included 80 ft of redwood and 50 ft of pine for a total cost of $339. Find the cost per foot of redwood and of pine.

Answer 1

Hey there!!

Let us take the price of the redwood as ' x ' and pine as ' y '

Then , we take it into an equation. We get,

50x + 80y = 285 -------------- ( 1 )

80x + 50y = 339 -------------- ( 2 )

Now, multiply the first equation with 8 and the second equation with 5

400x + 640y = 2280

400x + 250y = 1695

Now subtract the second equation from the first

390y = 585

y = 585 / 390

y = $1.5

Now substitute this into any equation

50x + ( 80 ) ( 1.5 ) = 285

50x + 120 = 285

50x = 165

x = 165 / 50

x = $3.3

Redwood = $3.3

Pine = $1.5

Hope helps!