# Math

Cindy had \$1.08 using 9 coins.
She had as many pennies as dimes.
___
Danielle had 96 coins, using ten coins.
She had the same number of nickels as all the other coins put together.

__
The coin choices are.
Half Dollar, Quarters, Dimes, Nickels, and Pennies.
Help?

1. 👍 0
2. 👎 0
3. 👁 250
1. Cindy had \$1.08 using 9 coins.
She had as many pennies as dimes.

There must be 4 pennies as 9 pennies would not allow for any other coins.

Since there are supposed to be as many dimes as there are pennies, 4P + 4D = 44 cents.

That leaves 65 cents to come from 1 coin which is impossible so there cannot be as many dimes as pennies.

10D + 9P = \$1.09 but 19 coins

1Q + 8D + 4P = \$1.09 but 13 coins

2Q + 5D + 4P = \$1.09 but 11 coins

3Q + 3 D + 4P = \$1.09 but 10 coins

3Q + 2D + 2N + 4P = \$1.09 but 11 coins

Halves must be involved

1H leaves 59 cents from 8 coins

Must have 4 pennies

1H + 4P leaves 55 cents from 4 coins

1H + 2Q + 1N + 4P = \$1.09 but 8 coins

1H + 1 Q + 3D + 4P = \$1.09 and 9 coins

Hooray!!!

1. 👍 0
2. 👎 0
2. Danielle had 96 cents, using ten coins.
She has the same number of nickels as all the other coins put together.

Based on our prior experience, it is rather easy to zero in on
1Q + 4D + 6N + 1P = 96 cents in 12 coins
where 6N = 1Q + 4D + 1P coins

1. 👍 0
2. 👎 0
3. Danielle had 96 cents, using ten coins.
She has the same number of nickels as all the other coins put together.

Based on our prior experience, it is rather easy to zero in on
1Q + 4D + 6N + 1P = 96 cents in 12 coins
where 6N = 1Q + 4D + 1P coins

OOPS - The hand was quicker than the eye. Lets try a more exact method.
Assuming no halves are involved.

1--25Q + 10CD + 5N + 1P = 96
2--Q + D + N + P = 10
3--N = Q + D + P
4--Substituting (3) into (1) yields 30Q + 15D + 6P = 96
5--Sustituting (3) into (2) yields Q + D + P = 5
6--Multiplying (5) by 6 yields 6Q + 6D + 6P = 30
7--Subtracting (6) from (4) yields 8Q + 3D = 22
8--Dividing through by the lowest coefficient yields 2Q + 2Q/3 = 1 + 3/7
9--(2Q - 1)/3 must be an integer as does (4Q - 2)/3
10--Dividing by 3 again yields Q + Q/3 - 2/3
11--(Q - 2)/3 is an integer k making Q = 3k + 2
12--Substituting back into (7( yields D = 2 - 8k
13--Clearly, k must be 0.
14--For k = 0, Q = 2 and D = 2.
15--From (5), P = 1 and hence, N = 4.
16--Thus we have Q = 2, D = 2, N = 5 and P = 1 and 2Q's + 2D's + 1P = 5N as coins go.
17--Also, 25(2) + 10(2) + 5(5) + 1(1) = 96 cents.

At last.!!!

1. 👍 0
2. 👎 0
4. Cindy has 1 half dollar,1quater,3 dimes,1 nickel,and 3 penny's.

1. 👍 0
2. 👎 0

## Similar Questions

1. ### Math

A bag contains twice as many pennies as nickels and four more dimes than quarters. Find all possibilities for the number of each coin if their total value is \$2.01. I have pennies = 4n nickels = n dimes = 4 + q quarters = q but I

2. ### math

find the 5 diff. ways a collection of 100 coins-pennies, dimes, and quarters- can be worth exactly worth \$4.99.

3. ### statistics

A jar contains 2 pennies, 6 nickels and 4 dimes. A child selects 2 coins at random without replacement from the jar. Let X represent the amount in cents of the selected coins. a. Find the probability X = 11. b. Find the expected

4. ### Math 120

Suppose there is a pile of quaters, dimes, an pennies with a total is \$1.06, How much of each coin can be present without being able to change for a dollar? If there are multiple selection of coins that will work

1. ### math

A charity organization is collecting change to raise monay. They have collected twice as many dimes as quarters, 22 more nickels than dimes, and 3 times as many pennies as nickels. a) define a variable for the number of quarters

2. ### Math

A charity organization is collecting change to raise money. They have collected three times as many dimes as quarters, 11 more nickels than dimes, and 2 times as many pennies as nickels. Let x represent the number of quarters.

3. ### ALGEBRA

Mae open her coin purse and found pennies,nickels and dimes with a total value of \$2.85.If there are twice as many pennies as there are nickels and dimes combined.How many pennies,dimes and nickels are there if she has a

4. ### Math

Assume that you select 2 coins at random from 5 coins: 3 dimes and 2 quarters. What is the probability that all of the coins selected are dimes?

1. ### math

A collection of coins has a value of 64 cents. There are two more nickels than dimes and three times as many pennies as dimes. How many of each kind of coins are there?

2. ### math

Julie is going to the mall. She has 15 coins in her pocket that nadd up to \$2.18. She has the same number of pennies as she does dimes. she has 5 more quarters than she has nickels. If she has 3 pennies, how many quarters, dimes

3. ### math

A jar contains 8 pennies, 3 nickels and 4 dimes. A child selects 2 coins at random without replacement from the jar. Let X represent the amount in cents of the selected coins. Find the expected value of X.

4. ### Math

A change purse contains an equal number of pennies, nickels, and dimes. The total value of the coins is 112 cents. How many coins of each type does the purse contain?