Worked examples
Two examples
Example 1
3 adult tickets and 2 child tickets cost $41. 1 adult and 4 child tickets cost $27. What does an adult ticket cost?
- 3a + 2c = 41 and a + 4c = 27.
- From the second, a = 27 − 4c. Then 3(27 − 4c) + 2c = 41: 81 − 10c = 41, so c = 4 and a = 11.
Answer: $11
Example 2
A jar has 30 dimes and quarters worth $4.80. How many quarters?
- q + d = 30 and 25q + 10d = 480.
- 25q + 10(30 − q) = 480, so 15q = 180 and q = 12.
Answer: 12
Where this is taught: Quiz 42: Lines, Slope, and Systems, “Two lines at once: a system”
The drill
Ten problems
This drill also has challenge problems. They use the same skill, set up the way the GED test sometimes sets up a problem, so that it looks new at first.
How many:
Type the number only; the unit is already there. Then press Check my answers at the bottom.Write each answer on the line. The answer key, with the reasoning, is on the last page.