1. Lesson 111: Three Statements of Equality

2. Many word problems contain three statements of equality
Many word problems contain three statements of equality. We can solve these problems by writing an equation for each statement of equality. If we have to use only three unknowns and if a solution to the system of the equations exists, it can be found by using substitution, elimination, or both.

3. Example: There were 26 nickels, dimes, and quarters in all, and their value was $2.25. How many coins of each type were there if there were 10 times as many nickels as quarters?

4. Answer: N + N + N = 26 5N + 10N + 25N = 225 10N = N N = 15 N = 10 N = 1
N D Q
N D Q
Q N D N Q

5. Example: The total number of blues, greens, and yellows in the pot was 7. the blues weighed 1 pound each, the greens weighed 4 pounds each, and the yellows weighed 5 pounds each. The total weight was 25 pounds. If there was 1 more yellow than green, how many of each color were there?

6. Answer: N + N + N = 7 N + 4N + 5N = 25 N + 1 = N N = 2 N = 3
B G Y
B G Y
G Y B Y G

7. HW: Lesson 111 #1-30