Calculate total frequency sum

Sum of all given frequencies must equal 85: $7 + 20 + x + 8 + y = 85$.

$x + y = 50$

Calculate class marks ($x_i$) and weighted sum

Class marks for 0-20, 20-40, 40-60, 60-80, 80-100 are 10, 30, 50, 70, 90 respectively. The sum of $f_i x_i$ is $7(10) + 20(30) + x(50) + 8(70) + y(90)$.

$\sum f_i x_i = 70 + 600 + 50x + 560 + 90y = 1230 + 50x + 90y$

Apply mean formula

Substitute values into the mean formula $\frac{\sum f_i x_i}{\sum f_i} = 66$: $\frac{1230 + 50x + 90y}{85} = 66$.

$1230 + 50x + 90y = 5610 \implies 50x + 90y = 4380 \implies 5x + 9y = 438$

Solve the system of linear equations

We have $x + y = 50$ (Equation 1) and $5x + 9y = 438$ (Equation 2). From Eq 1, $x = 50 - y$. Substituting into Eq 2: $5(50-y) + 9y = 438 \implies 250 + 4y = 438 \implies 4y = 188 \implies y = 47$. Then $x = 3$.

$x = 3, y = 47$

Calculate 5x + 3y

Substitute $x = 3$ and $y = 47$ into $5x + 3y$.

$5(3) + 3(47) = 15 + 141 = 156$