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.
The maximum amount can Carmen purchase so that after her store bucks and discount are applied is [tex]\boxed{\$ 110}.[/tex]
Further Explanation:
Given:
Carmen has [tex]\$ 30[/tex] in store bucks.
A [tex]25\%[/tex] discount coupon for a local department store.
The total amount should be less than [tex]\$ 60[/tex] before sales tax.
Explanation:
Consider the amount of the purchase as A.
The Carmen has [tex]\$ 30[/tex] in store bucks.
The new amount will be [tex]\left( {A - 30} \right).[/tex]
There is a [tex]25\%[/tex] discount coupon for a local department store.
The amount after discount can be calculated as follows,
[tex]\begin{aligned}{\text{Amount}} &= \left( {1 - 0.25} \right) \times \left( {A - 30} \right) \\&= 0.75\left( {A - 30} \right) \\\end{alignedd}[/tex]
The total amount should be less than [tex]\$ 60[/tex] before sales tax.
The maximum amount can Carmen purchases so that after her store bucks and discount are applied can be calculated as follows,
[tex]\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}[/tex]
The maximum amount can Carmen purchase so that after her store bucks and discount are applied is [tex]\boxed{\$ 110}.[/tex]
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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.
