1. Ms.lynch has 21 coins in nickels and dimes. Their total value is $1.65. How many of each coin does she have?

Question

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?

Answer 1

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

Answer 2

22 Dimes
8 quarters