Question

Roderick is counting the change on his dresser. He has twice as many pennies as he does dimes. He has twice the amount of dimes as he does nickels. He has 3 fewer quarters than dimes. Which variable definition would be easiest for Roderick to use when writing expressions for the number of all the coins?

x = number of pennies because the penny has the least value of all the coins.
x = number of nickels because there are fewer nickels than any other coin.
x = number of dimes because all the other coins are compared to dimes.
x = number of quarters because it has the greatest value of all the coins.

Answer 1

x=dimes because they are compared to all the others

Explanation:

If we didnt have dimes we couldnt calculate the rest of the coins

Answer 2

x = number of nickels because there are fewer nickels than any other coin.

Explanation:

Pennies = 2* Dimes

Dimes = 2*Nickels

Quarters = Dimes - 3

so

p = 2d

d = 2n

q = d - 3

q = 2n - 3

q + 3 = 2n = p/2

p = 2q + 6

n = (q + 3)/2

d = p/2 = q + 3

the least amount is n

n < d < p, so let x = n

p = 2q + 6

n = (q + 3)/2

d = p/2 = q + 3

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This is a better explanation here:

x = n =(q + 3)/2

2x - 3 = q

so...

q = 2x - 3

p = 2q + 6 = 2*(2x - 3) + 6 = 4x

n = ((2x - 3) + 3)/2 = x

d = q + 3 = 2x - 3 + 3 = 2x