Question

Fatima earned an 85 average in her science class. The average is based on 6 tests that she takes over the span of the marking period. On her first four tests she earned an 83, a 78, an 87, and an 80. On her sixth test she scored 8 points more than on her fifth test.
Let x be the score Fatima received on her fifth test. Set up an equation using x that models this scenario. Solve the equation and state what Fatima earned on her fifth and sixth tests.

Answer 1

Answer:

Fifth Score = 87

Sixth Score = 95

Step-by-step explanation:

Given

$Average = 85$

$Scores = 83, 78, 87, 80$

$Fifth\ score = x$

$Sixth\ Score = 8 + x$

Required

Set up an equation

Solve for the fifth and sixth score

Average is calculated as thus:

$Average = \frac{\sum x}{n}$

$Average = \frac{83 +78 + 87 + 80 + x + 8 + x}{6}$

Substitute 85 for Average

$85 = \frac{83 +78 + 87 + 80 + x + 8 + x}{6}$

$85 = \frac{83 +78 + 87 + 80 + 8+ x + x}{6}$

$85 = \frac{336+ 2x}{6}$

Multiply both sides by 6

$85 * 6 = 336 + 2x$

$510= 336 + 2x$

Solve for 2x

$2x = 510 - 336$

$2x = 174$

Solve for x

$x = 174/2$

$x = 87$

Hence:

$Fifth\ Score = 87$

$Sixth\ Score = 87 + 8$

$Sixth\ Score = 95$