Question

1A basketball player made 6 out of 12 free throws she attempted which is 50%. She wants to know how many consecutive free throws more in a row she would have to make to raise her overall successful baskets divided by total attempts or percent of successful free throws to 70%.

(a) Write an rational equation to represent this situation with the variable x as the UNKNOWN number of consecutive attempts needed to raise her average.

(b) Solve the equation for x, show steps algebraically. Solve and show how many consecutive free throws would she have to make to raise her percent to 70%?

Note: correct answer to part (a) has only one variable, the variable x. Need to set up a ratio and cross multiply to solve for x. X represents how many more consecutive tries she needs to make in a row to raise her overall average up to 70%​

Answer 1

(To represent this situation with the variable x as the number of consecutive attempts needed, we can set up the following rational equation:

(6 + x)/(12 + x) = 70/100

To solve the equation for x, we can cross multiply:

100(6 + x) = 70(12 + x)

600 + 100x = 840 + 70x

100x - 70x = 840 - 600

30x = 240

x = 8
Therefore, she would need to make 8 consecutive free throws in a row to raise her percent to 70%. Tadaaaaaaaaa