ddiego2628
Answered

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Diane is participating in a 6-day cross-country biking challenge. She biked for 54 , 50 , 47 , 55 , and 60 miles on the first five days. How many miles does she need to bike on the last day so that her average (mean) is 53 miles per day?

Sagot :

The formula for mean/average is m = sum of the terms/number of the terms. Basically, you add all the numbers provided and divide it by how many of them.

So our terms are 48, 54, 51, 69, 64. We are missing the last term, which the problem needs us to find, in order to meet the requirement of the average 58 miles per days, which is m.

Let's call the last term x.

m = sum of the terms/number of the terms

58 = (48 + 54 + 51 + 69 + 64 + x)/6

We need to work backward the formula to find x.

Because (48 + 54 + 51 + 69 + 64 + x) divided by 6 gives us the m, which is 58, we will multiply 58 by 6 to give us the sum of (48 + 54 + 51 + 69 + 64 + x)

58 * 6 = 348

So 348 is the sum of 48 + 54 + 51 + 69 + 64 + x. Let make it into an equation:

48 + 54 + 51 + 69 + 64 + x = 348. Now, simplify it by adding all the values except x.

286 + x = 348. Now what is left is to take 348 minus 286, which gives us 62.

Let's check by plugging 62 as x into the mean formula.

(48 + 54 + 51 + 69 + 64 + 62)/6 = m = 58

Hope this helps!

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