Question

When Nick shoots a basketball, he either sinks the shot or misses. For each shot Nick sinks, he is given 5 points by his father. For each missed shot, Nick's Dad takes 2 points away. Nick attempts a total of 28 shots and ends up with zero points (i.E., he breaks even). How many shots did Nick sink

Answer 1

Nick sinks 8 shots and misses 20 shots.

Explanation:

Let x be the number of shots Nick sinks. Nick attempts a total of 28 shots, then 28-x is the number of shots Nick misses.

Nick is given 5 points by his father for each shot he sinks, then he is given 5x points for x such shots.

Nick's Dad takes 2 points away for each missed shot, so he takes away 2(28-x) points for 28-x missed shots.

In total, Nick earnes
`5x-2(28-x)` points.

Nick ends up with zero points, so

`5x-2(28-x)=0\\ \\5x-56+2x=0\\ \\7x=56\\ \\x=8\\ \\28-8=20`

Hence, Nick sinks 8 shots and misses 20 shots.