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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.

Respuesta :

MrRoyal

Answer:

Fifth Score = 87

Sixth Score = 95

Step-by-step explanation:

Given

[tex]Average = 85[/tex]

[tex]Scores = 83, 78, 87, 80[/tex]

[tex]Fifth\ score = x[/tex]

[tex]Sixth\ Score = 8 + x[/tex]

Required

Set up an equation

Solve for the fifth and sixth score

Average is calculated as thus:

[tex]Average = \frac{\sum x}{n}[/tex]

[tex]Average = \frac{83 +78 + 87 + 80 + x + 8 + x}{6}[/tex]

Substitute 85 for Average

[tex]85 = \frac{83 +78 + 87 + 80 + x + 8 + x}{6}[/tex]

[tex]85 = \frac{83 +78 + 87 + 80 + 8+ x + x}{6}[/tex]

[tex]85 = \frac{336+ 2x}{6}[/tex]

Multiply both sides by 6

[tex]85 * 6 = 336 + 2x[/tex]

[tex]510= 336 + 2x[/tex]

Solve for 2x

[tex]2x = 510 - 336[/tex]

[tex]2x = 174[/tex]

Solve for x

[tex]x = 174/2[/tex]

[tex]x = 87[/tex]

Hence:

[tex]Fifth\ Score = 87[/tex]

[tex]Sixth\ Score = 87 + 8[/tex]

[tex]Sixth\ Score = 95[/tex]

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