Upolatr
Compound Inequalities: Practice
Sow crdent

Question 3 of 5
Select the correct answer.
Shelly is going shopping at the mall to buy 3 pairs of shoes. She has a coupon for off per pair of shoes after buying the first pair at ful price. Shelly is willing to spend to not including tax. If the shoes she purchases are all the same price, what is the least and most amount she can spend per pair?
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and
and 542
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Ask by Craig Ford. in the United States

Mar 29,2025

Question

Upolatr
Compound Inequalities: Practice
Sow crdent

Question 3 of 5
Select the correct answer.
Shelly is going shopping at the mall to buy 3 pairs of shoes. She has a coupon for off per pair of shoes after buying the first pair at ful price. Shelly is willing to spend to not including tax. If the shoes she purchases are all the same price, what is the least and most amount she can spend per pair?
and
and
and 542
and

Ask by Craig Ford. in the United States

Mar 29,2025

UpStudy AI · Accepted Answer

Let the full price per pair be $$ x $$. Shelly pays full price for the first pair and gets a discount for the other two, so the cost for the 3 pairs is:  
$$
x + (x-2) + (x-2) = 3x - 4.
$$

Since she is willing to spend between $$ \$80 $$ and $$ \$122 $$, we have the inequality:
$$
80 \leq 3x - 4 \leq 122.
$$

Add 4 to all parts of the inequality:
$$
80 + 4 \leq 3x \leq 122 + 4,
$$
which simplifies to:
$$
84 \leq 3x \leq 126.
$$

Next, divide everything by 3:
$$
\frac{84}{3} \leq x \leq \frac{126}{3},
$$
resulting in:
$$
28 \leq x \leq 42.
$$

Thus, the least amount Shelly can spend per pair is $$ \$28 $$ and the most is $$ \$42 $$.

Matching this with the answer choices, the correct answer is:  
$$ \$28 $$ and $$ \$42 $$.
Shelly can spend between \$28 and \$42 per pair of shoes.

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