Amanda bought g gallons of paint for $$ \$ 16.55 $$ per gallon and $$ t $$ pints of paint thinner for $$ \$ 5.97 $$ per pint. a. Write an expression to represent the total amount that Amanda spent. b. If Amanda bought 8 gallons of paint and 3 pints of paint thinner, how much did she spend? Explain your answer. A. $$ 16.55 \mathrm{t} \cdot 5.97 \mathrm{~g} $$ B. $$ 16.55 \mathrm{~g} \cdot 5.97 \mathrm{t} $$ C. $$ 16.55 \mathrm{t}+5.97 \mathrm{~g} $$ v. $$ 16.55 \mathrm{~g}+5.97 \mathrm{t} $$ b. Find how much Amanda spent for the given values. Amanda spent $$ \$ 16.55 $$. When 8 is substituted for g and $$ \square $$ is substituted for t , the expression simplifies to $$ \square $$. (Type integers or decimals.)

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UpStudy AI · Accepted Answer

Let's break down the problem step by step.

### Part a: Write an expression for the total amount spent

1. **Identify the costs:**
   - The cost of paint is $$ 16.55 $$ dollars per gallon, and Amanda bought $$ g $$ gallons. Therefore, the total cost for paint is $$ 16.55g $$.
   - The cost of paint thinner is $$ 5.97 $$ dollars per pint, and Amanda bought $$ t $$ pints. Therefore, the total cost for paint thinner is $$ 5.97t $$.

2. **Combine the costs:**
   - The total amount spent by Amanda can be expressed as the sum of the costs for paint and paint thinner:
   $$
   \text{Total Cost} = 16.55g + 5.97t
   $$

Thus, the expression representing the total amount that Amanda spent is:
$$
16.55g + 5.97t
$$

### Part b: Calculate the total amount spent for given values

1. **Substitute the values:**
   - Amanda bought $$ g = 8 $$ gallons of paint and $$ t = 3 $$ pints of paint thinner.
   - Substitute these values into the expression:
   $$
   \text{Total Cost} = 16.55(8) + 5.97(3)
   $$

2. **Calculate each term:**
   - Calculate the cost for paint:
   $$
   16.55 \times 8 = 132.4
   $$
   - Calculate the cost for paint thinner:
   $$
   5.97 \times 3 = 17.91
   $$

3. **Add the costs together:**
   $$
   \text{Total Cost} = 132.4 + 17.91 = 150.31
   $$

Thus, Amanda spent $$ \$ 150.31 $$.

### Summary of Answers
- The expression for the total amount spent is $$ 16.55g + 5.97t $$.
- When substituting $$ g = 8 $$ and $$ t = 3 $$, the total amount spent simplifies to $$ 150.31 $$.
a. The total amount Amanda spent is $$ 16.55g + 5.97t $$. b. Amanda spent \$150.31.

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