1. A basketball player made 15 out of 50 free throws she attempted which is 30%. 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 attempts or percent of successful free throws to 50%. (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 50%?

1 pt for correct answer to part (b), 4 pts for showing steps you took to get the correct answer and showing the formula with variable x that you used in part (a).
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 50%

The percentage of successful trials in an experiment is computed as

s

=

number of successful trails

total number of trails

The fraction  

s

is usually expressed on a scale of hundered:  

S

=

s

×

100

%

Answer and Explanation:

a

)

0.85

=

12

+

x

15

+

x

b

)

5

Given:

A basketball player made 12 out 15 free throws

She wants to make successive free throws to increase her percentage to  

85

%

At  

12

out of  

15

the success percentage of the player is:  

12

15

×

100

=

80

%

In order to increase her percentage to  

85

%

, let x be the number of free throws she has to make consecutively.

a)

She makes x out of x free throws, therefore, her successful attempts increase to  

12

+

x

and her number of attempts increase to  

15

+

x

.

The percentage of successful free throws now will be

S

=

12

+

x

15

+

x

×

100

This desired success percentage is 85%, that is  

S

=

85

, therefore,

85

=

12

+

x

15

+

x

×

100

0.85

=

12

+

x

15

+

x

(

1

)

The situation is represented by equation (1).

b)

The number of consecutive free throws (x) the player has to make is obtained by solving (1):

0.85

=

12

+

x

15

+

x

(

1

)

12

+

x

=

0.85

(

15

+

x

)

12

+

x

=

12.75

+

0.85

x

0.15

x

=

0.75

x

=

0.75

0.15

=

5

Therefore, the player has to make  

5

consecutive free throws.

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