Problema Solution

Translate the following situation into an equation. Do not solve.

“Profits in the fourth quarter for Company A were 78.2% of that of Company B. Profits in the fourth quarter for Company C were 103.8% of Company B’s profits. Together the three companies earned $324,300 in the fourth quarter. What were the profits for Company B?”

Answer provided by our tutors

Given: A = 0.782 x B C = 1.038 x B A + B + C = $324,300 Substitute the A and C values given in terms of B into the (A + B + C = $324,300) equation: [ (0.782 x B) + B + (1.038 x B) ] = $324,300 (2.82 x B) = $324,300 B = ($324,300 / 2.82) = $115,000 ---------------- Then you just back-substitute the value for B into the two first equations to get: A = (0.782 x B) = (0.782 x $115,000) = $89,930 C = (1.038 x B) = (1.038 x $115,000) = $119,370

logic=

1) Let the profit for Company B be $x

2) Hence profit for Company A is 78.2x/100 = $0.782x

3) And that Company C is 103.8x/100 = $1.038x

==> The total earning = x + 0.782x + 1.038x = $2.82x

==> 2.82x = $324,300

Solving the above, we will get x, which is company B's profits.