Question

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

Answer 1

Answer:

$110.

Step-by-step explanation:

Let x be the cost of item that Carmen purchased from departmental store.

We are told that Carmen has $30 in store bucks and a 25% discount coupon for a local department store. We are asked to find the cost of Carmen's purchase so that after her store bucks and discount are applied, her total is no more than $60 before sales tax.  

As the $30 store bucks are applied before the 25% discount is applied, so we need to find x such that x-30 minus 25% of (x-30) should be less than or equal to 60. We can represent this information in an equation as:

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

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

$x-30-(0.25x-7.5)\leq 60$    

$x-30-0.25x+7.5\leq 60$  

$0.75x-22.5\leq 60$  

$0.75x-22.5+22.5\leq 60+22.5$

$0.75x\leq 82.5$  

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

$x\leq 110$    

Therefore, Carmen should make purchases at-most for $110 so that her total is no more than $60 before, sales tax.

Answer 2

Answer:120

Step-by-step explanation:

120(.25)= 30

120-30= 90

90-30=60