WHAT IS THE ANSWER

Question

Janet has three times as many dimes as nickels and twice as many quarters as nickels. If she has $3.40 in all, how many nickels, dimes, and quarters does she have? If n represents the number of nickels Janet has, which of the following equations could be used to solve the problem?

Answer 1

25*Quarters     +   10*Dimes       +   5*Nickels         = 340               [note: everything in cents]

 25(2n)            +   10(3n)           +    5n                   = 340              [still in cents]

 

$0.25(2n)        +   $0.10(3n)       +   $0.05(n)           = $3.40

 

Once you solve for n, then q=2n and d=3n.

Answer 2

Hi Crystal, if we let n represent the number of nickels, then the number of dimes, d, is equal to 3n. The number of quarters, q, is equal to 2n.

 

Equation:

 

.10 * d + .25 * q + .05 * n = 3.40

 

Substitute:

 

Number of dimes, d = 3n.

 

Number of quarters, q = 2n.

 

.10 * 3n + .25 * 2n + .05 * n = 3.40

 

.30 * n + .50 * n + .05 * n = 3.40

 

.85 * n = 3.40

 

Divide both sides by .85:

 

n = 4

 

Janet has 4 nickels.

 

Janet has 3 times as many dimes as nickels, or 3 * 4, which equals 12.

 

Janet has 2 times as many quarters as nickels, or 2 * 4, which equals 8.

 

Check:

 

12 * .10 + 8 * .25 + 4 * .05 = 3.40

 

1.20 + 2.00 + .20 = 3.40

 

3.40 = 3.40

 

Values check.

 

Questions?

Answer 3

Well, you would have needed to list the potential equations for us to match, but I will make an attempt to answer the question anyway and hopefully one will match.

 

Let d = # of dimes, n = # of nickels, and q = # of quarters.

 

We know that she has three times as many dimes as nickels.  So d=3n.

 

We know that she has twice as many quarters as nickels.  So q=2n.

 

The key to writing an equation for this situation is to write an equation with all three variables and then replace two of them with equivalent expressions using n.

 

The total value is $3.40.  Since dimes are worth $0.10, the value of the dimes is 0.10d.  Since nickels are worth $0.05, the value of the nickels is 0.05n.  Finally, the value of the quarters is 0.25q since quarters are worth $0.25.  By adding up these three values, we get the total value:

 

0.10d + 0.05n + 0.25q = 3.40

 

Next, replace d with 3n and q with 2n,

 

0.10(3n) +0.05n + 0.25(2n) = 3.40

 

That might match the solution you are looking for, or they may have simplified it:

 

0.30n + 0.05n + 0.50n = 3.40

 

or

0.85n = 3.40