Question

Lucy earned $400 and $550 in interest the last 2 years. How much interest must she earn this year so that her average earnings over the three year period is more than $600? Show your work.

Answer 1

the average of "arithmetic mean" of a dataset is simply the "sum of the data" divided by the "amount of data", so if we had say

a, b, c

its average will be (a+b+c)/3

so, let's say Lucy will need to earn "x" to have an average of $600, so

`\bf \stackrel{\textit{average amount}}{\cfrac{400+550+x}{3}}=600\implies \cfrac{950+x}{3}=600\implies 950+x=1800\\\\\\x=1800-950\implies x=850`

so, if she earns that much more, she'll have an average of 600, and if she earns more than that, her average is "more than 600" then.

x ⩾ 850.