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 5eThe 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 15eThe 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!
