Answer:
Each envelope is $1.42
Step-by-step explanation:
Let, the cost of postcards = x and the cost of envelopes = y, in dollars.
It is given that,
First customer paid $12 for 14 postcards and 5 envelopes.
This gives, 14x + 5y = 12.
Second customer paid $24.8 for 10 postcards and 15 envelopes.
This gives, 10x + 15y = 24.8
We get the system of equations,
14x + 5y = 12
10x + 15y = 24.8
We multiply 1st equation by 3. This gives us the equations,
42x + 15y = 36
10x + 15y = 24.8
Subtracting both equations, we get,
32x = 11.2
i.e. [tex]x=\frac{11.2}{32}[/tex]
i.e. x = 0.35
Which gives,
10 × 0.35 + 15y = 24.8
i.e. 15y = 24.8 - 3.5
i.e. 15y = 21.3
i.e. [tex]y=\frac{21.3}{15}[/tex]
i.e. y = 1.42
Hence, the cost of each postcard is $0.35 and each envelope is $1.42.
