Question

The junior varsity football

team scored 23 points in last Saturday’s
game. They scored a combination of 7-
point touchdowns and 3-point field goals.
How many touchdowns and how many
field goals did they score?

Answer 1

1 touchdown and 3 field goals

Answer 2

2 touchdowns, 3 field goals

Explanation:

The number of touchdowns cannot be more than 3, so it is relatively easy to find the solution by trial and error.

23 is not divisible by 3, so 0 touchdowns is not a solution

23 -7 = 16 is not divisible by 3, so 1 touchdown is not a solution

23 -14 = 9 is divisible by 3, so 2 touchdowns and 3 field goals is a solution

21 -21 = 2 is not divisible by 3, so there is only one solution.