3. The next week, Maia earns \( \$ 37 \). She wants to use it to buy soccer shorts and 5 pairs o socks. The shorts she wants each cost \( \$ 22.05 \). a What do each pair of socks cost if Maia spends exactly \( \$ 37 \) on the socks and shorts? (In Maia's city, there is no sales tax.) Write and solve an equation if it helps you with your thinking. b Write an inequality to represent all the sock prices that Maia could afford with \( \$ 37 \).

Let's help Maia determine the cost of each pair of socks she can afford and establish the range of possible sock prices within her budget. ### **Given:** - **Total Budget:** \$37 - **Cost of Shorts:** \$22.05 each - **Number of Pairs of Socks:** 5 --- ### **Part a: Finding the Cost of Each Pair of Socks** **Objective:** Determine the cost per pair of socks if Maia spends exactly \$37 on shorts and socks. **Let:** - \( x \) = Cost of one pair of socks **Total Expenditure Equation:** \[ \text{Cost of Shorts} + \text{Cost of Socks} = \text{Total Budget} \] \[ \$22.05 + 5x = \$37 \] **Solving for \( x \):** 1. **Subtract the cost of shorts from both sides:** \[ 5x = \$37 - \$22.05 \] \[ 5x = \$14.95 \] 2. **Divide both sides by 5 to find the cost per pair of socks:** \[ x = \frac{\$14.95}{5} \] \[ x = \$2.99 \] **Answer:** Each pair of socks costs **\$2.99**. --- ### **Part b: Establishing an Inequality for Affordable Sock Prices** **Objective:** Write an inequality to represent all possible sock prices Maia can afford without exceeding her \$37 budget. **Let:** - \( x \) = Cost of one pair of socks **Total Expenditure Inequality:** \[ \text{Cost of Shorts} + \text{Cost of Socks} \leq \text{Total Budget} \] \[ \$22.05 + 5x \leq \$37 \] **Solving the Inequality for \( x \):** 1. **Subtract the cost of shorts from both sides:** \[ 5x \leq \$37 - \$22.05 \] \[ 5x \leq \$14.95 \] 2. **Divide both sides by 5 to find the maximum affordable cost per pair of socks:** \[ x \leq \frac{\$14.95}{5} \] \[ x \leq \$2.99 \] **Inequality Representation:** \[ x \leq \$2.99 \] **Interpretation:** Maia can afford any sock priced at **\$2.99 or less** per pair without exceeding her \$37 budget. --- ### **Summary** - **a.** Each pair of socks costs **\$2.99** when Maia spends exactly \$37. - **b.** Maia can afford socks priced at **\$2.99 or cheaper** per pair.