Question

Two customers went to a post office to buy postcards and large envelopes. Each postcard costs the same amount, and each large envelope costs the same amount. The first customer paid 19.20 for 14 postcards and 5 large envelopes. The second customer paid21.76 for 8 postcards and 12 large envelopes. What is the cost in dollars of each large envelope?

1) $1.97
2) $0.85
3) $0.95
4) $1.18

Answer 1

The cost of each large envelope is $1.18, determined by solving a system of equations that represents the total spent by each customer on postcards and large envelopes.

Step-by-step explanation:

To determine the cost of each large envelope, we can set up a system of equations based on the information provided about the purchases made by the two customers at the post office. We represent the cost of one postcard as x dollars and the cost of one large envelope as y dollars. From the first customer, we have the equation 14x + 5y = 19.20, and from the second customer, we have 8x + 12y = 21.76. Solving this system of equations, we will start by multiplying the first equation by 2 to eliminate x and solve for y. This gives us the new equation of 28x + 10y = 38.40. We then subtract the second customer's equation from this new equation to find y. The subtraction gives us 20x - 2y = 16.64. When we divide this equation by 2, we get 10x - y = 8.32. Using the first customer's original equation (14x + 5y = 19.20), we now have a simple system of two equations with two variables. Eventually, we solve to find that the cost of each large envelope (y) is $1.18.