Question

The swimming team has competed 45 races this season. They have won 30 races so far. How many races will the team need to win today for the team to have a 75% success rate?

Answer 1

Answer: 15 races

Proof of validity is shown below.

Answer 2

The team needs to win 15 races today.

Explanation:

The team has completed 45 races so far and has won 30 so far.

The current success rate is

`r = (30)/(45) * 100\% = 66.7\%`

We need this success rate to be 75%

Then the team must win a number x of races such that

`r = (30 + x)/(45 + x) = 0.75`

Now we solve the equation for x.

`(30 + x)/(45 + x) = 0.75\\\\30 + x=0.75(45 +x)\\\\30 + x=0.75(45) +0.75x\\\\x- 0.75x = 33.75-30\\\\0.25x = 3.75\\\\x= (3.75)/(0.25)\\\\x=15`

Finally the team need to win 15 carreras today