Answer:
A. Each large envelope costs $1.42
Step-by-step explanation:
To solve this, we want to set up a system of equations.
The first customer paid $12 for 14 postcards & 5 large envelopes.
- The total number of dollars paid is $12. This will be on one side of the equal sign.
- They bought 14 postcards. This will be represented by 14p.
- They bought 5 large envelopes. This will be represented by 5e
- The equation will be: 14p + 5e = 12
The second customer paid $24.80 for 10 postcards & 15 large envelopes.
- The total number of dollars paid is $24.80. This will be on one side of the equal sign.
- They bought 10 postcards. This will be represented by 10p.
- They bought 15 large envelopes. This will be represented by 15e
- The equation will be: 10p + 15e = 24.80
Now let's set up our equations together.
14p + 5e = 12
10p + 15e = 24.80
We will solve this through elimination. First we want to eliminate one variable at a time. We will start with e because we can see that 5 and 15 will simplify easily.
Multiply the first equation by -3 to cancel out the variable e.
-3(14p + 5e = 12) = -42p - 15e = -36
Now set this up for elimination.
-42p - 15e = -36
10p + 15e = 24.80
______________
-32p = -11.2
Divide both sides by -32.
p = 0.35
Each postcard costs $0.35.
Now that we know the value of p, let's plug it into one of equations to find e.
14p + 5e = 12
14(0.35) + 5e = 12
4.9 + 5e = 12
5e = 7.1
e = 1.42
Each large envelope costs $1.42
Check your answer by plugging both values back into the equation you haven't used yet.
10p + 15e = 24.80
10(0.35) + 15(1.42) = 24.80
3.5 + 21.3 = 24.80
24.80 = 24.80
Your answer is correct.
Hope this helps!
