Select the correct answer.

A teacher is buying supplies for an upcoming art project. She buys *x* bottles of paint for $1.29 each. She buys 8 more canvases than bottles of paint for $1.89 each. Her total pretax cost is $37.38. How many of each item is she buying?

**A.**

7 bottles of paint and 15 canvases

**B.**

8 bottles of paint and 16 canvases

**C.**

9 bottles of paint and 17 canvases

**D.**

17 bottles of paint and 8 canvases

We are given that the teacher buys:

- *x* bottles of paint at $1.29 each
- (x + 8) canvases at $1.89 each
- The total cost of both items is $37.38

The equation representing the total cost is:

\[
1.29x + 1.89(x + 8) = 37.38
\]

Let's solve this equation step by step.

1. Distribute the $1.89 over the term $x + 8$:

\[
1.29x + 1.89x + (1.89 \times 8) = 37.38
\]

2. Calculate $1.89 \times 8$:

\[
1.89 \times 8 = 15.12
\]

Now the equation becomes:

\[
1.29x + 1.89x + 15.12 = 37.38
\]

3. Combine like terms:

\[
(1.29x + 1.89x) = 3.18x
\]

Now the equation is:

\[
3.18x + 15.12 = 37.38
\]

4. Subtract 15.12 from both sides:

\[
3.18x = 37.38 - 15.12
\]

\[
3.18x = 22.26
\]

5. Solve for *x* by dividing both sides by 3.18:

\[
x = \frac{22.26}{3.18} = 7
\]

So, the teacher buys **7 bottles of paint**. Since she buys 8 more canvases than bottles of paint, the number of canvases is:

\[
x + 8 = 7 + 8 = 15
\]

Thus, the teacher buys **7 bottles of paint and 15 canvases**.

The correct answer is **A**.

Would you like more details or have any questions?

### Related Questions:
1. How would the equation change if the cost of paint was $1.50 instead of $

A teacher is buying supplies for an upcoming art project. She buys x bottles of paint for $1.29 each. She buys 8 more canvases than bottles of paint for $1.89 each. Her total pretax cost is $37.38. How many of each item is she buying?

A. 7 bottles of paint and 15 canvases
B. 8 bottles of paint and 16 canvases
C. 9 bottles of paint and 17 canvases
D. 17 bottles of paint and 8 canvases

Learn how to solve a linear equation involving the total cost of paint and canvases. This problem demonstrates key algebraic concepts, such as linear equations and cost calculation, with step-by-step guidance. Suitable for students in Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation