Question

Algebra
Brian has made 9 of 19 free throws so far this season.

His goal is to make 70% of his free throws.

If Brian makes his next x free throws in a row, the function f(x)=9+x19+xf(x)=19+x9+x​ represents Brian’s new ratio of free throws made.

How many successful free throws in a row will raise Brian's percent made to at least 70%?

Is this a reasonable answer? Explain.

Answer 1

SOLUTION

GIVEN

Brian has made 9 of 19 free throws so far this season.

His goal is to make 70% of his free throws.

If Brian makes his next x free throws in a row, the function f(x) = ( 9 + x) /( 19 + x ) represents Brian’s new ratio of free throws made.

TO DETERMINE

How many successful free throws in a row will raise Brian's percent made to at least 70% ?

Is this a reasonable answer

EVALUATION

Here it is given that the Brian has made 9 of 19 free throws so far this season.

His goal is to make 70% of his free throws.

If Brian makes his next x free throws in a row, the function f(x) = ( 9 + x) /( 19 + x ) represents Brian’s new ratio of free throws made.

So by the given condition

$\displaystyle \sf{f(x) = \frac{70}{100} }$

$\displaystyle \sf{ \implies \: \frac{9 + x}{19 + x} = \frac{70}{100} }$

$\displaystyle \sf{ \implies \: \frac{9 + x}{19 + x} = \frac{7}{10} }$

$\displaystyle \sf{ \implies \: 90 + 10x = 133 + 7x}$

$\displaystyle \sf{ \implies \: 3x = 43}$

$\displaystyle \sf{ \implies \: x = \frac{43}{3} }$

So value of x is not an integer

Now number of throws can not be fraction

Now an integer greater than 43/3 is 15

So required number of throws = 15

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