Advanced Algebra- Rational equation word problem

[AmyG]

I am studying for a test next week and was going through this problem and did not know how to approach this and solve this. Could someone please help me on how to approach this? Below is the question and the answer for the same.

I know I could start by 60/100 * 800 = 480 and 480+m/800+m = 0.65 and solve for m to get to the 65% and take it from there. But I am not sure how to approach the 4 out of 5 scenario here.

Here is the question -
XYZ is a terrible free throw shooter, averaging only 60% from the charity stripe over his career having shot 800 free throws. In order to be a more respected player, XYZ decides that he wants to get his free throw average to 65%. Assuming he makes 4 of every 5 free throws he shoots until the desired percentage is reached, how many free throws does XYZ need to shoot to achieve an average of at least 65%?

Here is the answer -
In order to average 65% from the free-throw line, XYZ needs to shoot 535 free throws of which he will make 428.

 

[Deleted member 4993]

I am studying for a test next week and was going through this problem and did not know how to approach this and solve this. Could someone please help me on how to approach this? Below is the question and the answer for the same.

I know I could start by 60/100 * 800 = 480 and 480+m/800+m = 0.65 and solve for m to get to the 65% and take it from there. But I am not sure how to approach the 4 out of 5 scenario here.

Here is the question -
XYZ is a terrible free throw shooter, averaging only 60% from the charity stripe over his career having shot 800 free throws. In order to be a more respected player, XYZ decides that he wants to get his free throw average to 65%. Assuming he makes 4 of every 5 free throws he shoots until the desired percentage is reached, how many free throws does XYZ need to shoot to achieve an average of at least 65%?

Here is the answer -
In order to average 65% from the free-throw line, XYZ needs to shoot 535 free throws of which he will make 428.

Your second equation is not correct.

If XYZ shoots 'm' more shots, then at the rate of (4/5), s/he will make (0.8 * m) baskets. Then your second equation becomes;

(480 + 0.8 * m)/(800 + m) = 0.65

Now solve for 'm' from the equation above.

 

[AmyG]

Your second equation is not correct.

If XYZ shoots 'm' more shots, then at the rate of (4/5), s/he will make (0.8 * m) baskets. Then your second equation becomes;

(480 + 0.8 * m)/(800 + m) = 0.65

Now solve for 'm' from the equation above.

Thank you so much! Using that new equation (480 + 0.8 * m)/(800 + m) = 0.65 I get m = 266.66 which is 267 when rounded.

But, It does not match the answer provided which is -
In order to average 65% from the free-throw line, XYZ needs to shoot 535 free throws of which he will make 428.

Is there more to this problem that I missing?!?

 

[Deleted member 4993]

Thank you so much! Using that new equation (480 + 0.8 * m)/(800 + m) = 0.65 I get m = 266.66 which is 267 when rounded.

But, It does not match the answer provided which is -
In order to average 65% from the free-throw line, XYZ needs to shoot 535 free throws of which he will make 428.

Is there more to this problem that I missing?!?

(480 + 428) / (800 + 535) = ?

(480 + 0.8*267) /(800 + 267) = ?

 

[AmyG]

Perfect! Looks like the provided answer key was wrong. With our approach, we get 65% (Equation 2 above) and that goes with the question, and with the answer key provided we get 68% (Equation 1) which is incorrect.

Thanks again for all the help with this.