Question

two customers went to a post office to buy postcards and envelopes. Each postcard costs the same amount, and each large envelope costs the same amount. The first customer paid $12 for 34 postcards and 5 large envelopes. The second customer paid $24.80 for 10 postcards and 15 large envelopes. What was the cost in dollars of each large envelpoe

Answer 1

The cost of 1 postcard is $0.12 and the cost of 1 large envelop is $1.58.

Explanation:

Let x be the cost of the postcard and y be the cost of the large envelop.

First customer paid $12 for 34 postcards and 5 large envelopes.

So, 34x + 5y = 12 --- (1)

Second customer paid $24.80 for 10 postcards and 15 large envelopes.

So, 10x + 15y = 24.8 --- (2)

Multiply the first equation by 3, we get,

(1) × 3 implies 102x + 15y = 36

(2) implies 10x + 15y = 24.8

Subtracting, we get,

92x = 11.2

x = 0.12

Substitute in (1), we get,

34(0.12) + 5y = 12

4.08 + 5y = 12

5y = 12 - 4.08

5y = 7.92

Divide both sides by 5.

y = 1.58

Hence, the cost of 1 postcard is $0.12 and the cost of 1 large envelop is $1.58.

Answer 2

The cost of postcard is $0.122 and the cost of large envelope is $1.57.

Explanation:

Let, the cost of postcards = x and the cost of large envelopes = y.

According to the question, we get the following system of equations,

34x + 5y = 12

10x + 15y = 24.80

We will now solve this system to obtain the value of x and y.

First, we divide second equation by 5,

34x + 5y = 12

2x + 3y = 4.96

Now, we multiply second equation by 17,

34x + 5y = 12

34x + 51y = 84.32

Subtracting the equations gives us,

-46y = -72.32 i.e. y = 1.57.

Substituting the vale of y in the first equation gives us,

34x + 5 × 1.57 = 12 i.e. 34x + 7.85= 12 i.e. 34x = 4.15 i.e. x = 0.122.

Hence, the cost of postcard is $0.122 and the cost of large envelope is $1.57.