Question

Emmanuel sent out 150 pieces of mail. Some of the letters required 40 cents postage while others required 64 cents. If the total postage bill was $71.04, how many pieces of each type were mailed?

Answer 1

Emmanuel mailed out 130 letters that required 40 cents postage and 20 letters that required 64 cents postage

Explanation:

To solve this problem, we can use a system of equations. Let's define two variables:

Let x be the number of letters that required 40 cents postage.

Let y be the number of letters that required 64 cents postage.

We know that the total number of letters sent out is 150, so we can write the equation:

x + y = 150

We also know that the total postage bill was $71.04. The cost of each letter that required 40 cents postage is 40x, and the cost of each letter that required 64 cents postage is 64y. So we can write another equation:

40x + 64y = 71.04

Now we have a system of equations. We can solve it using substitution or elimination. I will use elimination:

Multiply the first equation by 40:

40x + 40y = 600

Now subtract the second equation from the first:

(40x + 40y) - (40x + 64y) = 600 - 71.04

Simplifying:

-24y = -471.04

Divide both sides by -24:

y = 19.62666667

Since we can't have a fraction of a letter, we'll round this to the nearest whole number:

y = 20

Now substitute this value back into the first equation to find x:

x + 20 = 150

x = 130

Answer 2

104 pieces of mail were 40 cents

46 pieces of mail were 60 cents