Milton has four more dimes than nickels and four times as many quarters as dimes. The money is worth between ten and eleven dollars. How many of each kind of coin does he have?

Answer 1

Another way to look at it is to set up a formula with one variable.

Let n = number of nickels

n+4 = number of dimes

4(n+4) = number of quarters

Write an equation to multiply each expression with the value of the coin to get the total, x

x = (.05)n + (.10)(n+4) + (.25)(4)(n+4)

Multiply and distribute to simplify terms

x = .05n + .10n + .40 + n + 4

Combine like terms

x = 1.15n + 4.40

Since you have a range between 10 and 11, try the max for 11 as the value for x

11 = 1.15n + 4.40

Subtract 4.40 from each side

11-4.40 = 1.15n + 4.40-4.40

6.6 = 1.15n

Divide both sides by 1.15 to get number of nickels

6.6 ÷ 1.15 ≈ 5.74≈ n

Since you can’t have a fraction of a coin and it can’t be more than 11, round down to 5 and calculate the totals:

5 nickels = .25

5+4 dimes = 9 dimes = .90

4(9) quarters = 36 quarters = 9.00

.25 + .90 + 9.00 = 10.15

Answer 2

So Milton has 4 more dimes than nickels. That means that if he has 1 nickel, he has 4 more dimes, so he has 5 dimes (1+4 = 5). He also has 4 times as many quarters as dimes. So because he has one nickel and 5 dimes, he has 20 quarters (5x4=20).

1. 1 nickel 5 dimes 20 quarters
2. .05 cents + .50 cents + $5 = $5.55

What if he had 2 nickels.

1. 2 nickels 6 dimes 24 quarters
2. .10 cents + .60 cents + $6 = $6.70

You can continue this and put it in a table. But at this point we notice something. The quarters are always worth a lot more money than the other cents. We want between 10 and 11 dollars. Only using quarters how many do we need to get $10? 4 quarters is $1. We want $10 so 4x10 = 40 quarters.

Looking at the chart, if we want 40 quarters, how many dimes do we need? Because we multiply the number of dimes by 4 to get the number of quarters, we want 40 quarters, 10x4 = 40 so we want 10 dimes. How many nickels? Milton has 4 more dimes than nickels, so if he has 10 dimes, he has 6 nickels, because 6+4=10. Lets check how much money this is

1. 6 nickels 10 dimes 40 quarters
2. .30 cents + $1 +$10 = $11.30

It's a little bit too much. but we are very close. What if we just have one less nickel.

1. 5 nickels 9 dimes 36 quarters
2. .25 cents + .90 cents + $9 = $10.15

We have our answer. 5 nickels, 9 dimes and 36 quarters worth $10.15