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 $3.96 for 3 postcards and 2 large envelopes. The second customer paid $4.89 for 2 postcards and 3 large envelopes. What was the cost in dollars of each large envelope?

A) $0.30
B) $0.50
C) $0.45
D) $0.70

Answer 1

To find the cost of each large envelope, we need to solve a system of equations using the given information. The cost of each large envelope is $1.35.

Step-by-step explanation:

To find the cost of each large envelope, we need to set up a system of equations using the given information. Let's denote the cost of each postcard as X and the cost of each large envelope as Y.

From the first customer's purchase, we know that 3X + 2Y = $3.96. From the second customer's purchase, we know that 2X + 3Y = $4.89. We can solve this system of equations to find the values of X and Y.

Multiplying the first equation by 3 and the second equation by 2 gives us 9X + 6Y = $11.88 and 4X + 6Y = $9.78. Subtracting the second equation from the first equation, we get 5X = $2.10. Dividing both sides by 5, we find that X = $0.42. Substituting this value into the first equation, we can solve for Y. 3($0.42) + 2Y = $3.96. Simplifying, we get 1.26 + 2Y = $3.96. Subtracting 1.26 from both sides, we get 2Y = $2.70. Dividing both sides by 2, we find that Y = $1.35. Therefore, the cost of each large envelope is $1.35.