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Question

Difficulty: MediumLinear Inequalities in One Variable

An online retailer offers free shipping on orders of 75ormore.Acustomerhasplacedashirtcosting75 or more. A customer has placed a shirt costing 22.50 and a pair of pants costing 34.80intheirshoppingcart.Theywanttobuysomepairsofsocksthatcost34.80 in their shopping cart. They want to buy some pairs of socks that cost 4.50 per pair to qualify for free shipping. What is the minimum number of pairs of socks the customer must add to their cart to qualify for free shipping?

Answer: 4 pairs of socks

Answer

The minimum number of pairs of socks the customer must add to the cart is 4.
The customer needs to spend at least 75toqualifyforfreeshipping.Thecurrentsubtotalofthecartis75 to qualify for free shipping. The current subtotal of the cart is 22.50 + 34.80=34.80 = 57.30. The remaining amount needed to reach 75is75 is 75.00 - 57.30=57.30 = 17.70. Let ss represent the number of pairs of socks purchased at 4.50perpair.Thiscanberepresentedbytheinequality4.50 per pair. This can be represented by the inequality 4.50s \geq 17.70 .Dividingbothsidesoftheinequalityby. Dividing both sides of the inequality by 4.50 gives gives s \geq 3.93$. Since the customer cannot purchase a fraction of a pair of socks, the minimum number of pairs of socks they must purchase is 4.

Step-by-Step Solution

1
Calculate the total cost of the items already in the shopping cart.
22.50+22.50 + 34.80 = $57.30
To determine how much has already been spent before adding socks.
2
Set up an inequality to represent the total cost of the order including ss pairs of socks meeting the free shipping threshold of $75.
57.30+4.50s≥7557.30 + 4.50s \geq 75
The total cost of the shirt, pants, and socks must be greater than or equal to $75.
3
Subtract $57.30 from both sides of the inequality to find the minimum amount that needs to be spent on socks.
4.50s≥17.704.50s \geq 17.70
To isolate the term representing the cost of the socks.
4
Divide both sides of the inequality by $4.50 to find the minimum number of pairs of socks.
s≥3.93s \geq 3.93
To isolate the variable representing the number of pairs of socks.
5
Determine the smallest integer value of ss that satisfies the inequality.
4
The number of pairs of socks must be a whole number, and 4 is the smallest integer greater than or equal to 3.93.

Key Concept

Solving linear inequalities in one variable to find the minimum integer solution in a real-world context.
Estimated Time:1m 30s
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Topics

Linear Inequalities in One Variable

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