1 . irvin cut a 47 in. wire into two pieces. the longer piece is 13 in. longer than the shorter piece. what is the length of the longer piece?
2. maggie has only dimes and quarters in her purse. she has 27 coins with a total value of $4.05 in her purse. how many dimes does maggie have in her purse?

1. Let the shorter piece be x in. long
the longer piece will be x + 13 in. long
and the two pieces add up to be 47 in., so
x + ( x + 13 ) = 47
2x = 47 - 13
2x = 34
x = 17
the longer piece is x + 13 in. long,, or 17 + 13 = 30 in. long
 
2.  number of dimes: x
number of quarters: y
x + y = 27(1)
10x + 25y = 405...(2)
(1)*10: 10x + 10y = 270(3)
(2) - (3):15y = 135
y = 9
plug y = 9 into (1), you will find that x = 18
so 18 dimes, 9 quarters