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!
