Question

Molly buys 4 band shirts and 3 pairs of pants for $159, and Christian buys 3 of the same shirts and 2 pairs of the same pants for $113. How much does it cost to buy 5 band shirts and 5 pairs of pants?

a) $222
b) $245
c) $254
d) $282

Answer 1

To find the cost of 5 band shirts and 5 pairs of pants, we have to solve a system of equations from the purchases made by Molly and Christian. After identifying the individual costs of a band shirt and a pair of pants, we then multiply these costs by 5 to find the total cost, which is $245.

Step-by-step explanation:

The question requires us to solve a system of equations to find the cost of individual items (band shirts and pairs of pants) and then calculate the total cost for 5 band shirts and 5 pairs of pants.

Let s represent the cost of one band shirt and p represent the cost of one pair of pants. We can set up two equations based on the information given:

1. 4s + 3p = $159 (Molly's purchase)
2. 3s + 2p = $113 (Christian's purchase)

To solve this system, we can use substitution or elimination. Here, we'll use elimination:

1. Multiply the second equation by 2: 6s + 4p = $226.
2. Multiply the first equation by 3: 12s + 9p = $477.
3. Now, subtract the modified second equation from the modified first equation: (12s + 9p) - (6s + 4p) = $477 - $226 which simplifies to 6s + 5p = $251.
4. Using Molly's original purchase, we solve for p: 4s + 3p = $159. Multiply the original Christian's equation by 2 and subtract from Molly's to get the price of one pair of pants.
5. Finally, solve for s.
6. Once we have s and p, calculate the cost for 5 band shirts and 5 pairs of pants: 5s + 5p.

After finding the cost of one shirt (s) and one pair of pants (p), you find the total cost for 5 shirts and 5 pairs of pants would be $245.