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Nicholas has two times as many quarters as pennies and three times as many dimes as pennies. Nicholas has a total of forty-two pennies, dimes and quarters. The total value of the coins is $5.67. How many of each coin does he have?

 Jan 30, 2022
 #1
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2 = quarters

3 = dimes

total coins = 42

3 * 2 = 6

42 / 6 = 7

pennies = 7

7 * 2 = 14
quarters = 14

7 * 3 = 21

dimes = 21

 Jan 30, 2022
 #2
avatar+1214 
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Let p = the number of pennies, d = the number of dimes, and q = the number of quarters. We can set up a system of equatoins:

 

p + d + q = 42 (eq. 1)

q = 2p (eq. 2)

d = 3p (eq. 3)

p + 10d + 25q = 567 (eq. 4)

 

Plug in the results of equations 2 and 3 into equation 1.

 

p + 3p + 2p = 42

6p = 42

p = 7

d = 3p = 21

q = 2p = 14

 Jan 30, 2022

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