Question 1121565
Let C = The current grade sum of his previous 6 tests.
Let G = Be the grade needed on the 7th test


We can now write two equations.
Equation 1: {{{C/6 = 83.45}}}
Equation 2: {{{(C+G)/7 = 85}}}

Lets start by solving equation 1 for C:
{{{C/6 = 83.45}}}
Multiply both sides by 6
{{{6*(C/6) = 83.45*6}}}
Simplify
{{{highlight(C = 500.7)}}}

Now plug 500.7 into equation 2 for C
Equation 2: {{{(C+G)/7 = 85}}}
{{{(500.7+G)/7 = 85}}}
Multiply both sides by 7
{{{7*(500.7+G)/7 = 85*7}}}
Simplify
{{{500.7+G = 595}}}
Subtract 500.7 from both sides.
{{{highlight_green(G = 94.3)}}}

Folly will have to get a score of 94.3 on the next test.