Maria has a $400 gift certificate at a spa that she can use on massages or manic
ID: 1219643 • Letter: M
Question
Maria has a $400 gift certificate at a spa that she can use on massages or manicures. A massage costs $80, and a manicure costs $40.
a. Let x = massages. Let y = manicures. The equation for Maria’s budget constraint is:
___ = ___x +___ y
b. Suppose Maria decides to split her gift certificate with a friend and transfers half of the value of her gift certificate to her friend. The equation for her new budget constraint is:
___ = ____x +___ y
c. After giving away half of her gift certificate, suppose the price of massages increases by 50 percent before Maria can use her gift certificate. The equation for her new budget constraint is:
___ = ___x +___ y
Explanation / Answer
(a) Maria has a $400 gift certificate.
Total amount to spend = $400
Cost of a massage = $80
Number of massages = x
Cost of a manicure = $40
Number of manicures = y
Budget constraint can be stated as follows -
Total amount to spend = [Cost of a massage * Number of massages] + [Cost of a manicure * Number of manicures]
$400 = [$80 * x] + [$40 * y]
$400 = $80x + $40y
The equation for Maria's budget constraint is : $400 = $80x + $40y
(b) Maria has a $400 gift certificate. Now, she decides to split her gift certificate with a friend and transfer half the value of her gift certificate to her friend. The value left with Maria will now be $200.
Total amount to spend = $200
Cost of a massage = $80
Number of massages = x
Cost of a manicure = $40
Number of manicures = y
Budget constraint can be stated as follows -
Total amount to spend = [Cost of a massage * Number of massages] + [Cost of a manicure * Number of manicures]
$200 = [$80 * x] + [$40 * y]
$200 = $80x + $40y
The equation for Maria's budget constraint is : $200 = $80x + $40y
(c) Maria has a $400 gift certificate. Now, she decides to split her gift certificate with a friend and transfer half the value of her gift certificate to her friend. The value left with Maria will now be $200.
Price of massages increased by 50%.
Current price of a massage = $80
Increase = (50/100) * $80 = $40
New price = $80 + $40 = $120
Total amount to spend = $200
Cost of a massage = $120
Number of massages = x
Cost of a manicure = $40
Number of manicures = y
Budget constraint can be stated as follows -
Total amount to spend = [Cost of a massage * Number of massages] + [Cost of a manicure * Number of manicures]
$200 = [$120 * x] + [$40 * y]
$200 = $120x + $40y
The equation for Maria's budget constraint is : $200 = $120x + $40y