Question

Peter sent out a total of 150 envelopes. Some required a 44-cent stamp. the rest required 61-cents postage. If his total package cost was $74.50, determine how many envelopes were sent at each postage rate.

Answer 1

Let's call the number of envelopes that required a 44-cent stamp "x". Then the number of envelopes that required 61-cents postage is "150 - x".

The total cost of the 44-cent envelopes would be 0.44x, and the total cost of the 61-cent envelopes would be 0.61(150 - x).

We know that the total package cost was $74.50, so we can set up the equation:

0.44x + 0.61(150 - x) = 74.50

Simplifying and solving for x:

0.44x + 91.5 - 0.61x = 74.50
-0.17x = -17
x = 100

So Peter sent out 100 envelopes that required a 44-cent stamp, and 150 - 100 = 50 envelopes that required 61-cents postage.

Answer 2

Let's start by assigning variables to the unknowns in the problem. Let x be the number of envelopes that required a 44-cent stamp and y be the number of envelopes that required a 61-cent stamp. We know that the total number of envelopes is 150, so we can write an equation:

x + y = 150

We also know the cost of each type of envelope. If we multiply the number of envelopes by the cost per envelope, we should get the total cost of postage. Using this logic, we can write another equation:

0.44x + 0.61y = 74.50

Now we have two equations with two unknowns. We can solve this system of equations using substitution or elimination. Let's use substitution. Solve the first equation for x:

x = 150 - y

Now substitute this expression for x in the second equation:

0.44(150 - y) + 0.61y = 74.50

Simplify and solve for y:

66 - 0.44y + 0.61y = 74.50

0.17y = 8.50

y = 50

Now that we know y, we can substitute it back into either of the original equations to find x:

x + 50 = 150

x = 100

Therefore, Peter sent 100 envelopes that required a 44-cent stamp and 50 envelopes that required a 61-cent stamp.

Explanation: