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

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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
Each game token costs approximately \$0.17, and you can buy 6 tokens for \$1. For hay, each pound costs \$0.30, and you can purchase about 3.33 pounds for \$1.

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