Sandy bought 4 pears at "p" cents each and 6 oranges at 3 for $4. How much money did Sandy spend in all.  Sandy would prefer to spend all the money on 7 mangoes instead. How much money does each mango cost? Express your answer in dollars.

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The amount of money Sandy spent on pears is 4p cents, or, since 1 cent is 1/100 of a dollar, dollars.

The amount of money Sandy spent on oranges is $8. (She bought 6 oranges; 3 oranges cost $4.)

In all, Sandy spent dollars.

If she wants to spent this...

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The amount of money Sandy spent on pears is 4p cents, or, since 1 cent is 1/100 of a dollar, dollars.

The amount of money Sandy spent on oranges is $8. (She bought 6 oranges; 3 oranges cost $4.)

In all, Sandy spent dollars.

If she wants to spent this money on 7 mangoes, each mangoe must cost this amount divided by 7:

 

Each mango costs dollars.

 

Wait. I dont get it. Why are you multiplying 8*25. And why are you multiplying 25*7?

She multiplied the whole term by (25/25) to clear the denominator.  This is allowed because it is essentially multiplying the term by 1, thus not changing it.

Notice that (p/25) was multiplied by 25 to yield just p.  8 was multiplied by 25 and 7 was multiplied by 25 as well as another part of the process of multiplying the whole term by 25.

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The amount of money Sandy spent on pears is 4p cents, or, since 1 cent is 1/100 of a dollar, `4p/100 = p/25` dollars.

The amount of money Sandy spent on oranges is $8. (She bought 6 oranges; 3 oranges cost $4.)

In all, Sandy spent `8+ p/25 ` dollars.

If she wants to spent this money on 7 mangoes, each mangoe must cost this amount divided by 7:

`(8+p/25)/7= (8*25 + p)/(25*7)=(200+p)/175`

Each mango costs `(200+p)/175` dollars.

Approved by eNotes Editorial Team