Answer:
A)
There are 18 bushels of apples.
1 bushel of apples will make 20 quarts of apple cider.
1 bushel of apples will make 15 quarts of apple juice.
x = number of bushels to make cider out of.
y = number of bushels to make juice out of.
B)
As there are 18 bushels
x + y = 18
The apple farmer needs to produce a total of 330 quarts.
1 bushel of apples will make 20 quarts of apple cider.
1 bushel of apples will make 15 quarts of apple juice.
20x + 15y = 330
C)
x + y = 18. Thus we can express y in terms of x:
y = 18 - x
We can substitute the y in 20x + 15y = 330 and solve for x:
20x + 15 (18 - x) = 330
20x + 270 - 15x = 330
5x = 60
x = 12
And as y = 18 - x
y = 18 - 12
y = 6
[ C_1 ]: We could have done the same with x, expressing x in terms of y:
x = 18 - y, substitute the x in 20x + 15y = 330 and solve for y:
20 (18 - y) + 15y = 330
360 - 20y + 15y = 330
-5y = -30
y = 6
And as x = 18 - y
x = 18 - 6
x = 12
D)
As we had defined in A)
x = number of bushels to make cider out of
y = number of bushels to make juice out of,
there will 12 bushels of apples be processed into cider and
there will 6 bushels of apples be processed into juice
in order to produce
20 quarts of cider per bushel * 12 bushels = 240 quarts of cider, and
15 quarts of juice per bushel * 6 bushels = 90 quarts of juice,
which sum up to a total of
240 + 90 = 330 quarts of apple beverages, as required.
