math
posted by kathryn on .
1. Ms.lynch has 21 coins in nickels and dimes. Their total value is $1.65. How many of each coin does she have?
2. A vending machine that takes only dimes and quarters contains 30 coins, with a total value of $4.20. How many of each coin are there?

this is similar to the question I answered on the question after this:
pretend nickels=x
dimes=y
x+y=21 *total number of dimes and nickels is 21
.05x+.1y=$1.65 *the value of x is .5 and the value of y is .1 so when you multiply it by the number of x and y you get $1.65
now use elimination:
first solve for one variable
x+y=21
y=x+21
now plug "x+21" as "y" in the other equation
.05x+.1(x+21)=$1.65
.05x.1x+2.1=1.65 *distribute
.05x=.45
x=9
now plug 9 as x into the first equation
x+y=21
9+y=21
y=12
she has 9 nickels and 12 dimes
check by plugging in answers into both equations:
9+12=21 *correct
and
.05(9)+.1(12)=1.65 *correct
now apply the same concept to number 2 
22 Dimes
8 quarters