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Bloomington Nail Salon is having a special this month on services. Over the weekend, they performed 49 manicures and 16 pedicures, bringing in a total of $1,184 in receipts. So far this week, they have administered 31 manicures and 33 pedicures, with receipts totalling $1,321. How much does the salon charge for each service?

The salon charges $ for a manicure and $ for a pedicure.

Respuesta :

Answer: The salon charges $16 for a manicure and $25 for a pedicure.

Step-by-step explanation:

Let x represent the amount charged by the salon for a manicure.

Let y represent the amount charged by the salon for a pedicure.

Over the weekend, they performed 49 manicures and 16 pedicures, bringing in a total of $1,184 in receipts. It means that

49x + 16y = 1184- - - - - - - - - - 1

So far this week, they have administered 31 manicures and 33 pedicures, with receipts totalling $1,321. It means that

31x + 33y = 1321- - - - - - - - - - 2

Multiplying equation 1 by 31 and equation 2 by 49, it becomes

1519x + 496y = 36704

1519x + 1617y = 64729

Subtracting, it becomes

- 1121y = - 28025

y = - 28025/- 1121

y = $25

Substituting y = 25 into equation 1, it becomes

49x + 16 × 25 = 1184

49x + 400 = 1184

49x = 1184 - 400

49x = 784

x = 784/49

x = $16

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