Question

1. nissa earned an 87% on her unit 1 test, a 93% on her unit 2 test, and an 81% on her unit 3 test. after taking unit 4 test, her overall test average was an 88%. what did she earn on the unit 4 test?

1. solve for x.

\\(\frac{-12(x - 3) + 7}{5} = 17\\)

Explanation:

Problem 8

Step1: Recall the average formula

The average of \( n \) numbers \( x_1, x_2, \dots, x_n \) is \( \text{Average} = \frac{x_1 + x_2 + \dots + x_n}{n} \). Here, \( n = 4 \) (4 tests), average is \( 88\% \), and the first three scores are \( 87\%, 90\%, 81\% \). Let the Unit 4 score be \( x \).

Step2: Set up the equation

\( \frac{87 + 90 + 81 + x}{4} = 88 \)

Step3: Solve for \( x \)

First, multiply both sides by 4: \( 87 + 90 + 81 + x = 88 \times 4 \)
Calculate \( 88 \times 4 = 352 \) and \( 87 + 90 + 81 = 258 \)
Then, \( 258 + x = 352 \)
Subtract 258 from both sides: \( x = 352 - 258 = 94 \)

Step1: Eliminate the denominator

Multiply both sides of \( \frac{-13(x - 3) + 7}{5} = 17 \) by 5: \( -13(x - 3) + 7 = 17 \times 5 \)
Calculate \( 17 \times 5 = 85 \), so \( -13(x - 3) + 7 = 85 \)

Step2: Simplify the left side

Subtract 7 from both sides: \( -13(x - 3) = 85 - 7 = 78 \)

Step3: Solve for \( x \)

Divide both sides by -13: \( x - 3 = \frac{78}{-13} = -6 \)
Add 3 to both sides: \( x = -6 + 3 = -3 \)

Answer:

Nissa earned 94% on the Unit 4 test.

Problem 9