Question

In tennis, a first serve can be an ace, a fault, or it can be returned. In one match, a tennis player hit 24 aces, which was 25 of all her first serves. If 13 of her first serves were returned, how many of the tennis player's first serves were faults? 4 6 11 16

Answer 1

Answer:

16 faults

Step-by-step explanation:

The correct question is

In tennis, a first serve can be an ace, a fault, or it can be returned. In one match, a tennis player hit 24 aces, which was 2/5 of all her first serves. If 1/3 of her first serves were returned, how many of the tennis player's first serves were faults?

Let

x -----> the number of all her first servers

y ----> the number of first services returned

z ---> the number of first services faults

we know that

The number of aces plus the number of returned plus the number of faults must be equal to the number of all her first services

so

$x=24+y+z$

step 1

Find out the number of all her first servers

we have that

$24=\frac{2}{5}x$

Solve for x

$x=24(5)/2\\x=60\ first\ services$

step 2

Find out the number of first services returned

$y=\frac{1}{3}x$

substitute the value of x

$y=\frac{1}{3}(60)=20\ returned$

step 3

Find out the number of first services faults

$x=24+y+z$

we have

$x=60\\y=20$

substitute and solve for z

$60=24+20+z$

$60=44+z$

$z=16\ faults$