Shoot your shot! 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?

Nick sank 8 shots

Step-by-step explanation:

* Lets explain how to solve the problem

- Assume that Nick sinks x shots and misses y shots

- Nick attempts a total of 28 shots

- That means he sinks and misses 28 shots

∴ x + y = 28 ⇒ (1)

- His father give him 5 points (+5) for every sank shot and takes away

 2 points (-2) for every missed shot

- That means his score calculated by adding (the number of sank shots

  multiplied by 5) and (the number of missed shots multiplied by (-2))

- Nick ends up with zero points

∴ 5x + (-2)y = 0

- Remember: (+)(-) = (-)

∴ 5x - 2y = 0 ⇒ (2)

* Now we can solve the two equations by elimination method to find

 the number of sank shots

- Multiply equation (1) by 2 to eliminate y

∴ 2x + 2y = 56 ⇒ (3)

- Add equations (2) and (3)

∴ 7x = 56

- Divide both sides by 7

∴ x = 8

∵ x represents the number of sank shots

∴ Nick sank 8 shots