Question

1. A 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%?

Answer 1

(a) Let's denote the number of consecutive successful free throws needed as `x`. The equation to represent this situation would be:

`$$(6 + x)/(12 + x) = 0.7$$`

This equation represents the ratio of successful throws (6 successful throws she has already made plus `x` additional successful throws) to total throws (12 throws she has already attempted plus `x` additional attempts), which should equal 70% or 0.7.

(b) Now, let's solve this equation for `x`:

Step 1: Cross-multiply to get rid of the fraction:

`$$6 + x = 0.7 * (12 + x)$$`

Step 2: Distribute the 0.7:

`$$6 + x = 8.4 + 0.7x$$`

Step 3: Subtract `0.7x` from both sides:

`$$0.3x = 8.4 - 6$$`

Step 4: Simplify the right side:

`$$0.3x = 2.4$$`

Step 5: Divide both sides by `0.3` to solve for `x`:

`$$x = (2.4)/(0.3) = 8$$`

So, she would need to make **8 consecutive successful free throws** to raise her overall successful free throw percentage to **70%**.

Answer 2

Let’s solve this problem step by step:

(a) To represent this situation with a rational equation, let’s assume the number of consecutive successful free throws she needs to make is x. The total number of successful free throws would then be 6 + x, and the total number of attempts would be 12 + x. The rational equation representing this situation is:

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

Copy

(b) To solve the equation, we can cross-multiply and simplify:

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

600 + 100x = 840 + 70x

30x = 240

x = 8

Copy

Therefore, she would need to make 8 consecutive free throws to raise her percentage to 70%.

I hope this helps! Let me know if you have any further questions.

Explanation: