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 $12 for 14 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 envelope?
A $1.42 B $0.35 C $1.15
D
$0.63
Let's denote the cost of each postcard as x and the cost of each large envelope as y.
From the information given:
Customer 1 paid $12 for 14 postcards and 5 large envelopes.
So the total cost for Customer 1 can be expressed as:
12 = 14x + 5y
Customer 2 paid $24.80 for 10 postcards and 15 large envelopes.
So the total cost for Customer 2 can be expressed as:
24.8 = 10x + 15y
Now, we have a system of two equations:
14x + 5y = 12
10x + 15y = 24.8
We can solve this system of equations using the elimination method or substitution method. Let's use the substitution method:
From the first equation, we can express x in terms of y:
14x = 12 - 5y
x = (12 - 5y) / 14
Now substitute x into the second equation:
10((12-5y)/14) + 15y = 24.8
(120 - 50y) / 14 + 15y = 24.8
(120 - 50y + 210y) / 14 = 24.8
(160y + 120)/14 = 24.8
160y + 120 = 24.8 * 14
160y + 120 = 347.2
160y = 227.2
y = 227.2 / 160
y = 1.42
Therefore, the cost of each large envelope is $1.42. So the answer is A) $1.42.