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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 -

    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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