Kevin and randy muise have a jar containing 67 coins, all of which are either quarters or nickels. the total value of the coins in the jar is $9.15. how many of each type of coin do they have?

X= number of quarters
y= number of nickels

QUANTITY EQUATION
x + y= 67

COST EQUATION
$0.25x + $0.05y= $9.15

STEP 1
multiply quantity equation by -0.05

-0.05x - 0.05y= -3.35

STEP 2
add new step 1 equation to cost equation. Using elimination method to solve for x.

0.25x + 0.05y= 9.15
-0.05x - 0.05y= -3.35
y term "cancels out"

0.20x= 5.80
divide both sides by 0.20

x= 29 quarters

STEP 3
substitute x value in either original equation

x + y= 67

29 + y= 67
subtract 29 from both sides

y= 38 nickels

CHECK
$0.25x + $0.05y= $9.15
0.25(29) + 0.05(38)= 9.15
7.25 + 1.90= 9.15
9.15= 9.15

ANSWER: There are 29 quarters and 38 nickels.

Hope this helps! :)