A Alegbra question for smart people?

Question

ok this is the problem: A storekeeper goes to the bank to get 10 dollers worth of change. He requests twice as many quarters as half dollars, twice as many dimes as quarters, three times as many nickles as dimes, and no pennies or dollars. How many of each coin did the storekeeper get? Thanks so much if you can answer it....or at least sorta figure it out or at least just get an equation for it would be fine and i will find the answer if u can just get the equation.......Thanks

Answer 1

Total Amount = $10.00
Let Q = # of quarters
Let H = # of half dollars
Let D = # of dimes
Let N = # of nickles

Q = 2H or H = Q/2
D = 2Q
N = 3D
0.50H + 0.25Q + 0.10D + 0.05N = 10.00

Now you have four equations and four unknowns
Use the following equations and subtitute in the last equation:

D = 2Q
N = 2D = 3*2Q = 6Q
H = Q/2

0.50H + 0.25Q + 0.10D + 0.05N = 10.00
0.50(Q/2) + 0.25Q + 0.10(2Q) + 0.05(6Q) = 10.00
.25Q + .25Q + .20Q + .30Q = 10.00
Q = 10

Now subtitue Q in to find the other values:
D = 2Q = 2*10 = 20
N = 2D = 3*2Q = 6Q = 6*10 = 60
H = Q/2 = 10/2 = 5

Therefore there are:
10 Quarters
5 Half Dollars
20 Dimes
60 Nickles

There you go! ^_^

Answer 2

Just write everything in equations:

A storekeeper wants 10 dollars of change
change = 10.00
He has twice as many quarters as half dollars (the number of quarters is twice the number of half dollars)
quarters = 2 * half-dollars
Twice as many dimes as quarters
dimes = 2 * quarters
Three times as many nickels as dimes
nickels = 3 * dimes
And no pennies or dollars - this means that the only change he had was half-dollars, quarters, dimes and nickels.
So the total value of his change is
change = .50 * half-dollars + .25 * quarters + .10 * dimes + .05 * nickels.

So now we have a whole bunch of equations. It's possible to go into linear systems but that's overkill. Look at what we have:

We have an equation for nickels in terms of dimes. Substitute this:
change = .50 * half-dollars + .25 * quarters + .10 * dimes + .05 * (3 * dimes)
= .50 * half-dollars + .25 * quarters + .10 * dimes + .15 * dimes
= .50 * half-dollars + .25 * quarters + .25 * dimes

We have another equation for dimes in terms of quarters. Substitute again:
change = .50 * half-dollars + .25 * quarters + .25 * (2 * quarters)
= .50 * half-dollars + .75 * quarters
And for quarters in terms of half-dollars:
change = .50 * half-dollars + .75 * (2 * half-dollars) = 2.00 * half-dollars
So the two variables we're left with are "change" and "half-dollars". We know "change", though:
change = 10.00
10.00 = 2.00 * half-dollars
Obviously, there are 5 half-dollars. Now we can go back through the rest of the equations, substitute through, and find out how many quarters, nickels, and dimes there were.

Answer 3

The key here is looking at the relationships of the various denominations of coin.

Half Dollar = H
Quarter = Q
Dime = D
Nickle = N

Our shopkeeper receives an amount of half dollars (X). Since he wants twice as many quarters as half dollars, this amount can be represented by doubling the amount of half dollars (2X). Twice as many dimes as quarters can be represented by doubling the number of quarters (4X). Finally, the nickles are to be three times the number of dimes (12X). These facts and their relationship to the ten dollars can be written as the following equation.

(H * X) + (Q * 2X) + (D * 4X) + (N * 12X) = $10.00

Let convert all appropriate values to pennies. Which yields the following.

(50 * X) + (25 * 2X) + (10 * 4X) + (5 * 12X) = 1000

Carrying out the multiplication in the first phase gives us:

50X + 50X + 40X + 60X = 1000

Now we can combine like terms to get:

200X = 1000

I'll let you solve for X at this point and make the necessary calculations to determine the right amount of coins of each type.

Answer 4

You need to think about the number of each coin first, then the amount of money it represents.

Let x = the number of half dollars
let 2x = the number of quarters
let 4x = the number of dimes
let 12x = the number of nickels

if you have x half dollars you have 50x cents
if you have 2x quarters you have 50x cents
if you have 4x dimes you have 40x cents
if you have 12x nickels you have 60x cents

Add up all the cents. You have 200x cents. You also have a ten dollar bill which is 1000cents. Set them equal to each other.

200x=1000
x=5 so you have 5 half dollars, or $2.50
2x=10 so you have 10 quarters, or $2.50
4x=20 so you have 20 dimes, or $2.00
12x=60 so you have 60 nickels, or $3.00

Remember you are talking about 2 things, numbers and money. You have to keep them separate.

Answer 5

Remember, the value of the coins don't matter until you get the multiples right. Figure out what the equation is going to be first, then you'll have to guess and check until you get the answer. I'll help you 4 this though :

2h=q, 2q=d, 3d=n.

You should be able to understand that unless you're failing. This is a tough question, and no I'm not doing it for you. Why does everyone think that people are going to do their homework for then on Answers?

Answer 6

That means...
half dollars x 2= quarters
quarters x 2=dimes
dimes x 3=nickels
quarters + dimes + half dollars + nickels=10$
Now you just have to plug in...
If half dollars=1 then quarters=2 and dimes=4 and nickels=12... that adds up to... 2$ so that isn't it...

if half dollars=3 then quarters=6 and dimes=12 and nickels=36
That makes... 6$ so that isn't it either...

If half dollars=4 and quarters=8 then dimes=16 and nickels=48
That would equal... 8$

If half dollars=5 and quarters=10 then dimes=20 and nickels=60
That would be... 10$!!

Found it! your welcome! =)

Update:
Aww man how did someone find that out before me?

Answer 7

1) Q = 2H
2) D = 2Q
3) N = 3D
4) 50H + 25Q + 10D +5 N = 1000

You can substitute 2H for Q in equation 2 getting 4H, and then use this result for D in equation 3 so ypu can rewrite equation 4 all in terms of H.

Answer 8

5 half dollars 2.50
10 quarters 2.50
20 dimes 2.00
60 nickels 3.00

TOTAL 10.00

Answer 9

oh i got it. Get out a piece of paper. Write down ten dollars=
then figure out your own homework

Answer 10

I'm not so sure this is Algebra. Because I'm aceing Algebra and I don't even want o know, lol!