Question

In one day, a toy store sold 15 toy cars and 20 yo-yos for a total of $190. The next day, the toy store sold 3 toy cars and 12 yo-yos for a total of $102. What is the cost of one toy car?
$1 for one car
$2 for one car
$4 for one car
$8 for one car

Answer 1

Let's denote the price of one toy car as \( x \) dollars and the price of one yo-yo as \( y \) dollars.

From the sales data provided, we can set up the following two equations based on the sales totals:

1. From the first day:
\[
15x + 20y = 190
\]

2. From the second day:
\[
3x + 12y = 102
\]

Now, we can simplify each equation to make calculations easier.

Starting with the first equation, we can divide everything by 5:
\[
3x + 4y = 38 \quad \text{(Equation 1)}
\]

Then, simplifying the second equation by dividing everything by 3:
\[
x + 4y = 34 \quad \text{(Equation 2)}
\]

Next, we can eliminate \( y \). We can subtract Equation 2 from Equation 1 to do this:
\[
(3x + 4y) - (x + 4y) = 38 - 34
\]
This simplifies to:
\[
2x = 4
\]
So,
\[
x = 2
\]

Now that we have the cost of one toy car, we plug \( x \) back into Equation 2 to find \( y \):
\[
2 + 4y = 34
\]
Subtracting 2 from both sides gives:
\[
4y = 32
\]
Now, dividing by 4:
\[
y = 8
\]

Thus, the cost of one toy car is:
\[
\boxed{2}
\]