Cameron went into a grocery store and bought 4 apples and 7 mangos, costing a total of $17.75. Gavin went into the same grocery store and bought 2 apples and 5 mangos, costing a total of $10.75. Determine the price of each apple and the price of each mango.

Step-by-step explanation:

Let "a" and "m" represent the cost of an apple and a mango, respectively. Then Cameron's purchase can be represented as ...

  4a +7m = 17.75

Gavin's purchase can be represented as ...

  2a +5m = 10.75

Subtracting the first equation from twice the second gives ...

  2(2a +5m) -(4a +7m) = 2(10.75) -(17.75)

  3m = 3.75

  m = 1.25

Then the price of an apple can be found from the second equation:

  2a +5(1.25) = 10.75

  2a = 4.50 . . . . . . . . . . subtract 6.25

  a = 2.25 . . . . . . . . . . . divide by 2

The price of an apple was $2.25; the price of a mango was $1.25.

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