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musickatia [10]
3 years ago
6

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 pe

riod. 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.
Mathematics
1 answer:
LenaWriter [7]3 years ago
3 0

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:

<em></em>Fifth\ Score = 87<em></em>

<em></em>Sixth\ Score = 87 + 8<em></em>

<em></em>Sixth\ Score = 95<em></em>

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