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Jared and Zach are practicing their free throws. Jared attempted [tex] x [/tex] shots and made [tex] 75\% [/tex] of them. Zach attempted 10 more shots than Jared did and made [tex] 80\% [/tex] of them. Together, they made a total of 101 shots. Which equation represents this situation?

Select the correct answer.

A. [tex] 0.75 x = 0.8(x + 10) [/tex]

B. [tex] 0.75(x + 10) + 0.8 x = 101 [/tex]

C. [tex] 0.75 x + 0.8 x + 10 = 101 [/tex]

D. [tex] 0.75 x + 0.8(x + 10) = 101 [/tex]

Sagot :

GinnyAnsweridn
To determine which equation represents the given situation, we can translate the problem step by step into a mathematical equation.

1. Jared's made shots:
Jared attempted [tex]\( x \)[/tex] shots and made [tex]\( 75 \% \)[/tex] of them. Therefore, the number of shots Jared made is [tex]\( 0.75x \)[/tex].

2. Zach's made shots:
Zach attempted 10 more shots than Jared, so he attempted [tex]\( x + 10 \)[/tex] shots. Zach made [tex]\( 80 \% \)[/tex] of his attempts. Therefore, the number of shots Zach made is [tex]\( 0.8(x + 10) \)[/tex].

3. Total made shots:
Together, Jared and Zach made 101 shots. Thus, we can write the equation for the total number of made shots as the sum of Jared's and Zach's made shots:
[tex]\[ 0.75x + 0.8(x + 10) = 101 \][/tex]

This equation correctly combines the number of made shots from both Jared and Zach with the total number of shots they made together.

Therefore, the correct answer is:

[tex]\[ 0.75x + 0.8(x + 10) = 101 \][/tex]
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