Posted by **Tam** on Tuesday, October 22, 2013 at 6:01am.

Sophia buys an eqaul number of oranges and pears for a party. The oranges are bought at a price of 7 for $2 and the pears are bought at a price of 5 for $3. She pays $33 more for the pears than the oranges. How much does Sophia pay in all? How many oranges and pears does she buy altogether?

- Math -
**Henry**, Wednesday, October 23, 2013 at 5:04pm
X = # of oranges.

X = # of pears.

($2/7) * X = $Y

Multiply both sides by 7:

2x = 7y

Eq1: 2x - 7y = 0

($3/5) * X = y + 33

Multiply both sides by 5:

3x = 5y + 165

Eq2: 3x - 5y = 165

Multiply Eq1 by 3 and Eq2 by -2 and add:

+6x - 21y = 0

-6x + 10y = -330

Sum: -11y = -330

Y = $30 = Cost of oranges

Y+33 = 30 + 33 = $63 = Cost of pears

Total cost = 30+63 = $93.

In Eq1, replace y with 30:

2x - 7*30 = 0

2x = 210

X = 105 of each fruit.

Tot. fruit = 2*105 = 210.

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