Question

explanation:
write an expression to represent the number of shots each one made.
jared attempted x shots and made 75% of them, or 0.75x.
zach attempted 10 more shots than jared did, which is represented as x + 10. he made 80% of them, or 0.8(x + 10).
together, they made 101 shots. so, add the two expressions and set the sum equal to 101:
0.75x + 0.8(x + 10) = 101.

part b
question
using the scenario and your equation from part a, find the number of shots each player attempted.
type the correct answer in each box. use numerals instead of words.

jared attempted 40 shots.
zach attempted 50 shots.

Explanation:

Step1: Expand the equation

We start with the equation \(0.75x + 0.8(x + 10)=101\). First, distribute the \(0.8\) in \(0.8(x + 10)\):
\(0.75x+0.8x + 8 = 101\)

Step2: Combine like terms

Combine the \(x\)-terms: \(0.75x+0.8x=1.55x\), so the equation becomes:
\(1.55x + 8 = 101\)

Step3: Subtract 8 from both sides

Subtract 8 from each side to isolate the term with \(x\):
\(1.55x=101 - 8\)
\(1.55x = 93\)

Step4: Solve for x

Divide both sides by \(1.55\) to find \(x\):
\(x=\frac{93}{1.55}\)
\(x = 60\)

Step5: Find Zach's attempts

Zach attempted \(x + 10\) shots. Substitute \(x = 60\) into \(x + 10\):
\(60+10=70\)

Answer:

Jared attempted \(60\) shots.
Zach attempted \(70\) shots.