Question

Victoria spends 5/9 of her money of a flan and two chicken pies. Each chicken pie cost 1/6 as much as the flan. Victoria has $24 left.
a. How much money does Victoria spend?
b. How much does the flan cost?

Answer 1

M = Her money

If she spends 5 / 9 of her money the rest is 4 / 9 of her money.

Victoria has $24 left means:

4 M / 9 = $24

Multiply both sides by 9

4 M = $216

Divide both sides by 4

M = $54

Victoria spend 5 * $54 / 9 = $30

F = Price of flan

C = Price of chicken pie

Each chicken pie cost 1 / 6 as much as the flan means:

C = F / 6

Victoria spends 5 / 9 of her money of a flan and two chicken pies means:

5 M / 9 = F + 2 C

Replace C = F / 6 in this equation

5 M / 9 = F + 2 * F / 6

5 M / 9 = F + 2 * F / 2 * 3

5 M / 9 = F + F / 3

5 M / 9 = 3 F / 3 + F / 3

5 * 54 / 9 = 4 F / 3

$ 270 / 9 = 4 F / 3

$ 30 = 4 F / 3

Multiply both sides by 3

$ 90 = 4 F

Divide both sides by 4

$22.5 = F

F = $22.5

a.

Victoria spend $30

b.

The flan cost $22.5