In order to determine the number of nickels Jon has, it is ncessary to write the given situation in an algebraic way.
If x is the number of quarters, y the number of dimes and z the number of nickels, then, 0.25x + 0.1y + 0.05z is the total amount of money Jon has.
The value of the money john has is $1.75, then you have:
0.25x + 0.1y + 0.05z = 1.75 (1)
There are two more dimes than quarters:
y = x + 2
z = 2y = 2(x + 2) = 2x + 4
replace the previous expressions for y and z into the equation (1) and solve for x:
0.25x + 0.1y + 0.05z = 1.75
0.25x + 0.1(x + 2) + 0.05(2x + 4) = 1.75 apply distribution property
0.25x + 0.1x + 0.1(2) + 0.05(2x) + 0.05(4) = 1.75
0.25x + 0.1x + 0.2 + 0.1x + 0.2 = 1.75 order like terms
0.25x + 0.1x + 0.1x + 0.2 + 0.2 = 1.75 simplify like terms left side
0.45x + 0.4 = 1.75 subtract 0.4 both sides
0.45x = 1.75 - 0.4
0.45x = 1.35 divide by 0.45 both sides
x = 1.35/0.45
x = 3
To determine the number of nickels, replace x into the expression for z:
z = 2x + 4
z = 2(3) + 4
z = 6 + 4
z = 10
Hence, Joh has 10 nickels
