5. The best buy for game tokens is \( \$ 20 \) for 120 tokens. Find the unit rates. How much will each token cost? How many tokens can be purchased for \( \$ 1 \) ? 6. A 40-pound bale of hay costs \( \$ 12 \). Find the unit rates. How much hay can be purchased for \( \$ 1 \) ? How much does 1 pound of hay cost? pat

Let's solve each problem step by step. ### Problem 5: Game Tokens **Known Conditions:** - Cost for 120 tokens: \( \$ 20 \) **Step 1: Find the cost per token.** To find the cost of each token, we divide the total cost by the number of tokens: \[ \text{Cost per token} = \frac{\text{Total Cost}}{\text{Number of Tokens}} = \frac{20}{120} \] **Step 2: Calculate the cost per token.** Now, let's perform the calculation: \[ \text{Cost per token} = \frac{20}{120} = \frac{1}{6} \approx 0.1667 \] So, each token costs approximately \( \$ 0.1667 \). **Step 3: Find how many tokens can be purchased for \( \$ 1 \).** To find out how many tokens can be purchased for \( \$ 1 \), we take the reciprocal of the cost per token: \[ \text{Tokens for } \$ 1 = \frac{1}{\text{Cost per token}} = \frac{1}{\frac{1}{6}} = 6 \] Thus, you can purchase 6 tokens for \( \$ 1 \). ### Problem 6: Bale of Hay **Known Conditions:** - Cost for 40 pounds of hay: \( \$ 12 \) **Step 1: Find the cost per pound of hay.** To find the cost of each pound of hay, we divide the total cost by the number of pounds: \[ \text{Cost per pound} = \frac{\text{Total Cost}}{\text{Weight in Pounds}} = \frac{12}{40} \] **Step 2: Calculate the cost per pound.** Now, let's perform the calculation: \[ \text{Cost per pound} = \frac{12}{40} = \frac{3}{10} = 0.3 \] So, each pound of hay costs \( \$ 0.3 \). **Step 3: Find how much hay can be purchased for \( \$ 1 \).** To find out how much hay can be purchased for \( \$ 1 \), we take the reciprocal of the cost per pound: \[ \text{Pounds for } \$ 1 = \frac{1}{\text{Cost per pound}} = \frac{1}{0.3} \approx 3.33 \] Thus, you can purchase approximately 3.33 pounds of hay for \( \$ 1 \). ### Summary of Results: - For game tokens: - Cost per token: \( \$ 0.1667 \) - Tokens for \( \$ 1 \): 6 tokens - For hay: - Cost per pound: \( \$ 0.3 \) - Pounds for \( \$ 1 \): approximately 3.33 pounds