Questions: A bus token costs 1.75. a. You spend 15.75 on tokens. Write and solve an equation to find how many tokens you purchase. 15.75 / 1.75 = T = 9 b. If you purchase 10 tokens, you get 2 free tokens. Write and solve an equation to find the approximate reduced price of each token when c. You also receive free tokens if you purchase 20 tokens. The reduced price for each token is 1.40. Write and solve an equation to find how many free tokens you receive when purchasing this special.

Solution Steps

a. To find how many tokens you can purchase with $15.75, divide the total amount spent by the cost of one token.

b. To find the reduced price per token when you get 2 free tokens for purchasing 10, calculate the total number of tokens received and divide the total cost by this number.

c. To find how many free tokens you receive when the reduced price per token is $1.40 for purchasing 20 tokens, set up an equation where the total cost divided by the total number of tokens (including free ones) equals $1.40, and solve for the number of free tokens.

To determine how many tokens were purchased with a total expenditure of \( \$15.75 \), we use the equation: \[ T = \frac{15.75}{1.75} = 9 \] Thus, the number of tokens purchased is \( T = 9 \).

When purchasing 10 tokens and receiving 2 free tokens, the total number of tokens received is: \[ \text{Total Tokens} = 10 + 2 = 12 \] The reduced price per token can be calculated as: \[ \text{Reduced Price} = \frac{10 \times 1.75}{12} \approx 1.4583 \]

For the case of purchasing 20 tokens at a reduced price of \( \$1.40 \), we first calculate the total cost: \[ \text{Total Cost} = 20 \times 1.75 = 35.00 \] Next, we find the total number of tokens received: \[ \text{Total Tokens} = \frac{35.00}{1.40} = 25 \] The number of free tokens received is: \[ \text{Free Tokens} = 25 - 20 = 5 \]

Final Answer