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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.

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Nonicorp1

Answer:

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. 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
  2. 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
  3. 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

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