sam has twice as many dimes as quarters and two less nickels than dimes. If sam has a total of$ 5.40. if sam has a total of 5.40, how many of each coin does he have If sam has a total of $ 5.40.

Quarters=10 coins

Dimes = 20 coins

Nickels=18 coins

Step-by-step explanation:

a). Find how many of each coin he has.

Let the number of quarters he has=x, number of dimes is twice that of quarters = (2*x) = 2x, number of nickels is 2 less than dimes=2x-2

So the number of each coin can be expressed as;

Quarters=x

Dimes=2x

Nickels=2x-2

b). Value of each coin

1 Quarter=$0.25, therefor the total value of the quarters Sam has = Number of Quarters*value of each quarter = (x*0.25) = $0.25x 1 Dime=$0.10, therefor the total value of the dimes Sam has=Number of Dimes*value of each dime = (2x*0.10) = $0.20x 1 Nickel=$0.05, therefor the total value of the nickels Sam has=Number of Nickels*value of each Nickel = (2x-2) 0.05 = (0.1x-0.1)

c). Total value for all the coins

Total value of Sams coins=Total value of Quarters+Total value of Dimes+Total value of Nickels

Replacing;

5.4 = (0.25x+0.20x+0.1x) - 0.1

5.4=0.55x-0.1

0.55x=5.4+0.1

0.55x/0.55=5.5/0.55

x=10

d). Replacing to get the number of each coin Sam has

Quarters=x=10 coins

Dimes=2x = (2*10) = 20 coins

Nickels=2x-2 = (2*10) - 2=18 coins