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Beth made wristbands and belts for a craft sale. She sold 30 of these items. Each wristband sold for $5.50. Each belt sold for $8.75. If Beth made $204 at the craft sale, how many wristbands did she sell? How many belts did she sell? Write and solve a system of equations to solve the problem. Show your work

Question

Beth made wristbands and belts for a craft sale. She sold 30 of these items. Each wristband sold for 5.50.Eachbeltsoldfor5.50. Each belt sold for 8.75. If Beth made $204 at the craft sale, how many wristbands did she sell? How many belts did she sell? Write and solve a system of equations to solve the problem. Show your work

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Solution

Let's denote the number of wristbands as W and the number of belts as B.

From the problem, we have two equations:

  1. W + B = 30 (This is because the total number of items sold is 30)

  2. 5.5W + 8.75B = 204 (This is because the total money made is 204,witheachwristbandcosting204, with each wristband costing 5.50 and each belt costing $8.75)

We can solve this system of equations by substitution or elimination. I'll use substitution:

First, solve the first equation for W: W = 30 - B

Then, substitute W into the second equation: 5.5(30 - B) + 8.75B = 204

Expand and simplify: 165 - 5.5B + 8.75B = 204

Combine like terms: 3.25B = 39

Finally, solve for B: B = 12

Substitute B = 12 into the first equation to solve for W: W = 30 - 12 = 18

So, Beth sold 18 wristbands and 12 belts.

This problem has been solved

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