Question

A customer at a store paid $12 for two large churros and three small churros. A second customer paid $8 more than the first customer for six large churros and one small churro. The price of each large churro is the same, and the price of each small churro is the same. What is the cost of each large churro, and what is the cost of each small churro?

Answer 1

Each large churro costs $4, and each small churro costs $2.

Step-by-step explanation:

Let's assign variables to the unknowns in the problem:

Let L be the price of each large churro,

And let S be the price of each small churro.

From the first customer's purchase, we can create the equation:

2L + 3S = 12

From the second customer's purchase, we get the equation:

6L + S = 12 + 8 = 20

Now, we can solve these two equations simultaneously to find the values of L and S.

Multiplying the first equation by 2, we can eliminate the L terms:

4L + 6S = 24

Subtracting this equation from the second equation gives:

6L + S - (4L + 6S) = 20 - 24

2L - 5S = -4

Next, we can multiply the first equation by 5 and subtract it from the second equation:

5(2L + 3S) - (6L + S) = 5(12) - 20

10L + 15S - 6L - S = 60 - 20

4L + 14S = 40

Now, we have a system of two equations:

2L - 5S = -4

4L + 14S = 40

We can solve this system by substitution or elimination to find:

L = 4

S = 2

Therefore, each large churro costs $4, and each small churro costs $2.