Question

a group of bandys students go out to lunch at jimador mexican grill in denver. if two have burritos and 5 has tacos, the bill will be 19.50. if five have burritos and two have tacos, the bill 22.50. find the price of a taco and the price of a burrito.

Answer 1

To find the price of a taco and the price of a burrito, we can set up a system of equations. Let's define:

- \( b \) = price of a burrito
- \( t \) = price of a taco

Based on the information provided, we can set up the following two equations:

1. For the first scenario (2 burritos and 5 tacos):
\[
2b + 5t = 19.50
\]

2. For the second scenario (5 burritos and 2 tacos):
\[
5b + 2t = 22.50
\]

Now we can solve this system of equations. We'll start with the first equation:

1. \( 2b + 5t = 19.50 \)
- Multiply the entire equation by 2 to make elimination easier later:
\[
4b + 10t = 39.00 \quad \text{(Equation 1')}
\]

2. The second equation is:
\[
5b + 2t = 22.50 \quad \text{(Equation 2)}
\]

Next, we can multiply the second equation by 5 to align it with Equation 1':
\[
25b + 10t = 112.50 \quad \text{(Equation 2')}
\]

Now we can subtract Equation 1' from Equation 2':
\[
(25b + 10t) - (4b + 10t) = 112.50 - 39.00
\]
\[
21b = 73.50
\]
\[
b = \frac{73.50}{21} = 3.50
\]

Now that we have the price of a burrito, we can substitute \( b \) back into one of the original equations to find the price of a taco. Using the first equation:
\[
2b + 5t = 19.50
\]

Substituting \( b = 3.50 \):
\[
2(3.50) + 5t = 19.50
\]
\[
7.00 + 5t = 19.50
\]
\[
5t = 19.50 - 7.00
\]
\[
5t = 12.50
\]
\[
t = \frac{12.50}{5} = 2.50
\]

Thus, the prices are:
- Price of a burrito (\( b \)) = $3.50
- Price of a taco (\( t \)) = $2.50