Answer:
85
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