Question

A carpenter purchased 70 ft of redwood and 80 ft of pine for a total cost of $351. A second purchase, at the same prices, included 100 ft of redwood and 60 ft of pine for a total cost of $420. Find the cost per foot of redwood and of pine.

Answer 1

Hey there!!

Let us take the cost of 1 feet redwood as ' x '

Let us take the cost of 1 feet pine as ' y '

For the first scenario :

70 ft red wood and 80 ft pine

1 feet redwood - $x

70 feet redwood - $70x

1 feet pine - $y

80 feet pine - $80y

Total = $351

70x + 80y = 351 --------------------------------- ( 1 )  

Second scenario :

1 feet redwood - $x

100 feet redwood - $100x

1 feet pine - $y

60 feet pine - $60y

total - $420

100x + 60y = 420 ----------------------- ( 2 )

Now let us get both the equations together :

70x + 80y = 351 ------------- ( 1 )

100x + 60y = 420 ------------- ( 2 )

Now let us multiply the  the 1st equation with 3 and the 2nd equation with 4

3 ( 70x + 80y ) = 3 ( 351 )

4 ( 100x + 60y ) = 4 ( 420 )

............................

210x + 240y = 1053

400x +  240y = 1680

...........................

Now let us subtract the first equation from the second ...

400x + 240y = 1680

- ( 210x + 240y ) = - ( 1053 )

......................

190x = 627

dividing by 160 on both sides

x = 627 / 190

x = 3.3

The cost for 1 feet or per foot for the redwood is $3.3

Now substitute the value of x in any given given equation and find out y

I will substitute in the 1st equation

70x + 80y = 351

70 ( 3.3 ) + 80y = 351

231 + 80y = 351

Subtracting by 231 on both sides

80y = 351 - 231

80y = 120

dividing by 80 on both sides

y = 120 / 80

y = 1.5

The cost for 1 feet or per foot for the pine = $1.5

The answers - $3.3 ( redwood ) ; $1.5 ( pine )

Hope my answer helps!