Gabby has entered a cooking contest with 6 rounds. In order to earn a medal, she needs a final average score higher than 75. After the first five rounds, her average score is 78. What must her score be in the sixth (final) round to earn a medal? Show your work and answer in a complete sentence.

85

Step-by-step explanation:

We will use the formula

xbar = \sum Xi/N

xbar is the average

N is the number of rounds

\sum Xi is sum of rounds

From the formula:

\sumXi = xbar × N.

If Gabby has entered a cooking contest with 6 rounds and in order to earn a medal, she needs a final average score higher than 75, this means that;

N = 6

xbar = 75+x (since her average needs to be more than 75)

Substitute in the formula

\sumXi = 6(75+x) 1

If after the first five rounds, her average score is 78, then:

At N = 5, xbar = 78

Substitute into the formula

\sumXi = 5(78)

\sumXi = 390 2

First we need to get x by equating equation 1 and 2:

6(75+x) = 390

450 + 6x = 390

6x = 390-450

6x = -60

x = -10

Taking x as 10

Since she needs 75+x to earn the medal, substitute x = 10 into the expression:

This means that she will need average score of 75+10 i.e 85 to win the medal

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step-by-step explanation:

b. x + 1

step-by-step explanation:

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