applicatinos of linear systems

Question

sent out a total of 150 envelopes, some required a 44 cent stamp. the rest required 61 cents postage. if his total postage cost was 74.50. determine how many envelopes were sent at each postage rate

Answer 1

Hi Tanner, we'll start by setting up our system of equations, with x and y representing the number of each envelope. The setup would be as follows:

x + y = 150

0.44x + 0.61y = 74.5

Using substitution, isolate y and solve for x:

y = 150 - x

0.44x + 0.61(150 - x) = 74.5

0.44x + 91.5 - 0.61x = 74.5

-0.17x = -17

x = 100

Solve for y:

y = 150 - 100

y = 50

So 100 were sent at 44 cents while 50 were sent at 61 cents.

Hope that helps!