Question

Antonio and Candice had the same amount of money to spend at the Artist Emporium. Antonio paid $35 for a large paint set and was able to buy 4 small canvases with the rest of his money. Candice paid $24 for a small paint set and was able to buy 6 small canvases. Both Antonio and Candice ended up spending all their money.
Which equation can you use to find c, the price of each canvas?
What is the price of each canvas?

Answer 1

Let's denote the amount of money that Antonio and Candice each had as \( M \), and let \( c \) be the price of each small canvas.

First, we can express Antonio's total spending:

1. Antonio paid $35 for a large paint set.
2. With the remaining money, he bought 4 small canvases, which cost \( 4c \).

So, we can write the equation for Antonio's spending as:
\[
M = 35 + 4c
\]

Next, we can express Candice's total spending:

1. Candice paid $24 for a small paint set.
2. With the remaining money, she bought 6 small canvases, which cost \( 6c \).

Thus, we can write the equation for Candice's spending as:
\[
M = 24 + 6c
\]

Since both Antonio and Candice spent the same amount of money, we can set the two equations equal to each other:
\[
35 + 4c = 24 + 6c
\]

Now, let's solve for \( c \):
1. First, we get all the terms involving \( c \) on one side and the constant terms on the other side:
\[
35 - 24 = 6c - 4c
\]
\[
11 = 2c
\]
2. Now, divide both sides by 2:
\[
c = \frac{11}{2} = 5.5
\]

Thus, the price of each small canvas is **$5.50**.