Question

Andrew has a collection of soda bottles. Some of them are 12 ounce bottles, and others are 16 ounce bottles. If the collection contains 20 bottles, which hold a combined 300 ounces, how many of the soda bottles are 12-ounce bottles?

Answer 1

Use a for the 12 ounce bottles and b for the 16 ounce bottles. Now make two equations, one to show total ounces and one total bottles.
12a + 16b = 300 (12 ounces in a number of bottles plus 16 ounces in b number of bottles it 300 total bottles).
a + b = 20 (total number of bottles.)
Now use the substitution method to solve for a, the number of 12 ounce bottles:
a + b = 20
- a - a
b = 20 - a (substitute 20 - a into the other equation for b)
12a + 16(20 - a) = 300 (Use distributive method
12a + 320 - 16a = 300 (Combine a's and subtrace 320)
- 320 - 320
-4a = -20 (Divide by -4)
a = 5
There are 5 12 ounce bottles.