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

The maximum amount can Carmen purchase so that after her store bucks and discount are applied is $\boxed{\ 110}.$

Further Explanation:

Given:

Carmen has $\ 30$ in store bucks.

A $25\%$ discount coupon for a local department store.

The total amount should be less than $\ 60$ before sales tax.

Explanation:

Consider the amount of the purchase as A.

The Carmen has $\ 30$ in store bucks.

The new amount will be $\left( {A - 30} \right).$

There is a $25\%$ discount coupon for a local department store.

The amount after discount can be calculated as follows,

$\begin{aligned}{\text{Amount}} &= \left( {1 - 0.25} \right) \times \left( {A - 30} \right) \\&= 0.75\left( {A - 30} \right) \\\end{alignedd}$

The total amount should be less than $\ 60$ before sales tax.

The maximum amount can Carmen purchases so that after her store bucks and discount are applied can be calculated as follows,

$\begin{aligned}0.75\left( {A - 30} \right) &\leqslant 60 \\\frac{{0.75\left( {A - 30} \right)}}{{0.75}} &\leqslant \frac{{60}}{{0.75}} \\ A - 30 &\leqslant 80 \\A - 30 + 30 &\leqslant 80 + 30 \\A &\leqslant 110 \\\end{aligned}$

The maximum amount can Carmen purchase so that after her store bucks and discount are applied is $\boxed{\ 110}.$

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Answer details:

Grade: High School

Subject: Mathematics

Chapter: Linear inequality

Keywords: Tax, returns, filed, tax return, Carmen, store bucks, department store, maximum, dollar, amount, Carmen purchase, discount, 25% discount coupon, coupon, sales tax.

Answer 2

Answer:

$110

Step-by-step explanation:

Let x represent the amount of the purchase.  Since the $30 in store credit is applied before the 25% discount, we first subtract 30 from the price:

x-30

Taking a 25% discount means that Carmen pays 100-25 = 75% of the price.  75% = 75/100 = 0.75; this gives us

0.75(x-30)

Since it can be no more than 60, we use the inequality "less than or equal to"; this gives us

0.75(x-30) ≤ 60

Using the distributive property,

0.75(x)-0.75(30) ≤ 60

0.75x - 22.5 ≤ 0

Add 22.5 to each side:6

0.75x - 22.5 + 22.5 ≤ 60+22.5

0.75x ≤ 82.5

Divide each side by 0.75:

0.75x/0.75 ≤ 82.5/0.75

x ≤ 110

The largest purchase price she can afford is $110.