Question

1. A basketball player made 12 out of 15 free throws she attempted. She wants to know how many consecutive free throws she would have to make to raise the percent of successful free throws to 85% (a) Write an equation to represent this situation. (b) Solve the equation. How many consecutive free throws would she have to make to raise her percent to 85%?​

Answer 1

Answer:

She would need to make 5 consecutive free successful throws

Step-by-step explanation:

Equations

A basketball player wants to improve his percent of successful throws to 85%.

She currently has made 12 out of 15 free throws, which gives a success percentage of 12/15*100=80%

So, she needs a number of free consecutive free throws to increase that number to the desired target.

The percentage of success can be calculated as:

$\displaystyle P=\frac{\text{successful throws}}{\text{total throws}}*100$

Let's assume x is the number of required consecutive successful throws. Since she has already thrown 15 times, out of which has had 12 successful throws, now she will have 15+x total throws and 12+x successes, thus the new percentage is:

$\displaystyle P=\frac{12+x}{15+x}*100$

And this percentage must be equal to 85%, thus:

$\displaystyle \frac{12+x}{15+x}*100=85$

a) The equation to represent the situation is:

$\mathbf{\displaystyle \frac{12+x}{15+x}*100=85}$

b) Let's solve it.

Multiply by 15+x:

$\displaystyle (12+x)*100=85(15+x)$

Dividing by 5:

$\displaystyle (12+x)*20=17(15+x)$

Operating:

$\displaystyle 240+20x=255+17x$

Subtracting 17x and 240:

$\displaystyle 20x-17x=255-240$

Simplifying:

$\displaystyle 3x=15$

Dividing by 3:

x = 5

She would need to make 5 consecutive free successful throws

Answer 2

The number of throws is an illustration of proportions.

The number of free throws to raise her percent to 85% is 5

(a) The equation

The proportion is given as: 12 out of 15.

Let the number of throws be n.

So, the proportion would be:

$\mathbf{Proportion = \frac{12 + n}{15 + n}}$

To make 85% success, then the proportion must equal 85%.

So, we have:

$\mathbf{\frac{12 + n}{15 + n} = 85\%}$

(b) The solution to the equation

In (a), we have:

$\mathbf{\frac{12 + n}{15 + n} = 85\%}$

Express 85% as decimal

$\mathbf{\frac{12 + n}{15 + n} = 0.85}$

Cross multiply

$\mathbf{12 + n = 0.85(15 + n)}$

$\mathbf{12 + n = 12.75 + 0.85n}$

Collect like terms

$\mathbf{n -0.85n= 12.75 -12 }$

$\mathbf{0.15n= 0.75}$

Divide both sides by 0.15

$\mathbf{n= 5}$

Hence, the number of free throws to raise her percent to 85% is 5

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