Sarah and Owen Hebert purchased 26 stamps, a mixture of 13 cents and 22 cents stamps. Find the number of each type of stamp if they spent $4.19.

17 = 13 cent stamps

9 = 22 cent stamps

Step-by-step explanation:

Here is what we know:

a = 13 cent stamps

b = 22 cent stamps

Total stamps: 26

Total cost $4.19

Now we make equations based on what we know.

a + b = 26

13a + 22b = 419

Now we have to change the first equation so we can solve for the second. To do this, we have to find a similar factor for one of the variables. Let's change a.

Multiply the first equation by 13

13(a + b) = 13(26)

13a + 13b = 338

Now we put the two equations together and subtract. (Don't forget to change all the signs when you subtract)

   13a + 22b = 419

 - 13a -  13b  = - 338

=   0   +  9b   = 81

Solve for b.

9b = 81

b = 9

Plug b into the first equation to get a.

a + b = 26

a + 9 = 26

a = 17

17 = 13 cent stamps

9 = 22 cent stamps

You are done!

Hope this helped! :)

5x+2x=49

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