Question

what score must gaith get on his final project in order to get an average of 90% in the class?

a. 87%
b. 93%
c. 90%
d. 95%

Explanation:

Step1: Calculate the weighted sum of known grades

The weighted sum of tests, quizzes and homework is \(86\times0.4 + 94\times0.2+89\times0.1\).

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Step2: Set up an equation for the overall average

Let \(x\) be the grade on the final project. The overall average formula is \(0.4\times86+0.2\times94 + 0.1\times89+0.3x=90\). Substitute the value of \(62.1\) from step 1 into the equation: \(62.1+0.3x = 90\).

Step3: Solve for \(x\)

Subtract \(62.1\) from both sides: \(0.3x=90 - 62.1=27.9\). Then divide both sides by \(0.3\): \(x=\frac{27.9}{0.3}=93\).

Answer:

B. 93%