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

Fifth Score = 87

Sixth Score = 95

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 = (\sum x)/(n)`

`Average = (83 +78 + 87 + 80 + x + 8 + x)/(6)`

Substitute 85 for Average

`85 = (83 +78 + 87 + 80 + x + 8 + x)/(6)`

`85 = (83 +78 + 87 + 80 + 8+ x + x)/(6)`

`85 = (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`