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gavmur
5 days ago
7

Carmen has $30 in store bucks and a 25% discount coupon for a local department store. What maximum dollar amount can Carmen purc

hase so that after her store bucks and discount are applied, her total is no more than $60 before sales tax? (Note: The $30 store bucks are applied before the 25% discount is applied.)
Mathematics
2 answers:
babunello [3.6K]5 days ago
7 0

Answer: 120

Step-by-step explanation:

120 x 0.25 = 30

120 - 30 = 90

90 - 30 = 60

lawyer [4K]5 days ago
3 0

Answer:

$110.

Step-by-step explanation:

Let x represent the cost of the item that Carmen bought from the department store.

Carmen possesses $30 in store bucks along with a 25% discount coupon for a local department store. Our goal is to determine the maximum cost for Carmen's purchase such that after applying her store bucks and discount, her total remains at or below $60 before sales tax.

Since the $30 in store bucks is deducted prior to applying the 25% discount, we need to find x such that x - 30 minus 25% of (x - 30) must be less than or equal to 60. This can be set up as an equation:

x-30-((x-30)\times\frac{25}{100})\leq 60

x-30-((x-30)\times 0.25)\leq 60

x-30-(0.25x-7.5)\leq 60

x-30-0.25x+7.5\leq 60

0.75x-22.5\leq 60

0.75x-22.5+22.5\leq 60+22.5

0.75x\leq 82.5

\frac{0.75x}{0.75}\leq \frac{82.5}{0.75}

x\leq 110

Thus, Carmen's purchases should total no more than $110 before sales tax.

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