Mary needs to send out some letters and postcards. She went online at the United States Postal Service webpage and found out that it cost 45 cents to mail a letter and 35 cents to mail a postcard. Mary wrote to 15 people and the cost of postage was $6.15. If it cost 35 cents to mail a postcard and 49 cents to mail a letter, how many letters and how many postcards did he send?

Answer:6 postcards and 9 letters

Step-by-step explanation:

First we label what we are looking for

Label number of postcard sent as x

Label number of letter sent as y

The we know Mary wrote to 15people, either as postcard or letter, so from this we make an equation

x + y = 15 (1)

The we know the amount Mary used to send all this is $6.15 which is also 615 cents

Then we know sending one postcard is 35cents, and we labeled number of postcards to be x

So total amount used for postcard will be 35x

And we know sending one letter is 45 cents, and we labeled number of letters to be y

So total amount used for letter will be 45y, so adding all this will be equals to the total amount used which is given as $6.15 also 615 cents, so making another equation

35x + 45y = 615 (2)

Solving the two simultaneously equations

x + y = 15 (1)

35x + 45y = 615 (2)

So we make y the subject of formula in (1)

y = 15 - x (3)

So we put (3) in (2)

Anywhere we see y, we put 15-x

35x + 45 (15-x) = 615

35x + 675 - 45x = 615

35x - 45x = 615 - 675

-10x = - 60

divide both sides by - 10

x = 6

So therefore, number of postcards is 6

Then we put x = 6 in (3)

y = 15 - x

y = 15 - 6

y = 9

So therefore number of letters is 9