ALANZO HAS A JOB TRANSPORTING DRINKS

Question

Alonzo has a job transporting soft drinks by truck. His truck is filled with cans that weigh
14
ounces each and bottles that weigh
70
ounces each. There is a combined total of
850
cans and bottles in his truck.
Let
x
be the number of
14
-ounce cans in his truck. Write an expression for the combined total weight (in ounces) of the cans and bottles in his truck.

Answer 1

Let the number bottles be x, and let the number of cans be y.

We have the given total number of bottles and cans: 850.

Symbolically, we have the expression x + y = 850.

This would mean that:
y = 850 - x, or x = 850 - y -- because we need to express the total weight in terms of one variable.  Choose one of these.

We then have the expression 70x + 14y, which we would use to calculate the total weight of truckload of bottled and canned drinks.

Substituting for y in terms of x, we have:

70x + 14 (850 - x) = 70x + 11900 - 14x = 56x + 11900

Alternatively, substituting x in terms of y, we have:

70 (850 - y) + 14y = 59500 - 70y + 14y = 59500 - 56y

Were we given a combined total weight, a constant number, W, we could then state one of the following:

56x + 11900 = the total weight, W
59500 - 56y = the total weight, W

Once we solved for x or y, we would solve for the other. That is, if we solved for x, then we solve for y: y = 850 - x.

If we solved for y, we then solve for x: x = 850 - y.

We should verify the sum of these to equal 850.