M + 4 = -12

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

hram777 [196]

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 $\boxed{\$ 110}.$

Learn more:

Learn more about inverse of the function brainly.com/question/1632445.
Learn more about equation of circle brainly.com/question/1506955.
Learn more about range and domain of the function brainly.com/question/3412497

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.

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