MATH PROBLEM...NEED HELP...please..?

Question

1. A bank contains 30 coins, consisting of nickels, dimes, and quarters. There are twice as many nickels as quarters and the remaining coins are dimes. If the total value of the coins is $3.35, what is the number of each type of coin in the bank?

2. John, Dan, Karen, and Beth went to a costume ball. They chose to go as Anthony, Cleopatra, Romeo and Juliet. John got the costumes for Romeo and Cleopatra, but not his own costume. Dan saw the costumes for Juliet and Himself. Karen went as Anthony. Beth drove two of her friends, who were dressed as Anthony and Cleopatra, to the ball. What costumes did each person wear?
tnx a lot..

Answer 1

1.
Let n be the number of nickels
Let d be the number of dimes
Let q be the number of quarters

Number of coins is 30:
#1) n + d + q = 30

There are twice as many nickels as quarters:
#2) n = 2q

Total value of the coins is $3.35. (Use the value in cents, rather than dollars).
#3) 5n + 10d + 25q = 335

Three equations and three unknowns...

Substitute #2 into #1:
d + 3q = 30
And into #3:
10d + 35q = 335

Now solve for d:
d = 30 - 3q

Substitute into the last one:
10(30 - 3q) + 35q = 335
300 - 30q + 35q = 335
5q = 35
q = 7

Plug q back into d = 30 - 3q:
d = 30 - 3(7)
d = 9

Plug q back into n = 2q
n = 2(7)
n = 14

So you have 14 nickels, 9 dimes, 7 quarters

(As a double check --> 0.70 + 0.90 + 1.75 = 3.35)

2.
Karen is Anthony (statement #3)
Since Karen is Anthony, John must be Juliet (statement #1)
Beth is not Cleopatra, so she must be Romeo (statement #4)
That leaves Dan to be Cleopatra.

Final result:
Karen = Anthony
John = Juliet
Beth = Romeo
Dan = Cleopatra

Those cross-dressing friends...

Answer 2

N nickels, D dimes, Q quarters

1) N + D + Q = 30
2) N = 2Q
3) 5N + 10D + 25Q = 335

Substitute from equation 2 into equations 1 & 3, giving two equations in two unknowns

1) 2Q + D + Q = 30
1a) D + 3Q = 30

3) 5(2Q) + 10D + 25Q = 335
3a) 10D + 35Q = 335

Multiply 1a by 10 and subtract from 3a

10D + 35Q = 335
10D + 30Q = 300
---------------------
5Q = 35
Q = 7
N = 14
D = 30 - 7 - 14 = 9

Here I think you ned to set up a table with peoples names on one axis and costumes along the other. Then carefully read the information and use it to put a Yes or No into cells where a name and costume intersect. This will lead you to the truth.

Perhaps costumes across the page (rows) and people down the page (columns).

Simple example: Karen went as Anthony - put a Y under Anthony for Karen, put N's for the other people in the Anthony column and for the other costumes in Karen's row.

Good luck

Answer 3

1. Let x = # of quarters
y = # of nickels
z = # of dimes

Then 25x + 5y + 10z = 335, x+y+z = 30, and y=2x. So you have two equations for x and z,

35x + 10z = 335
3x + z = 30

Multiply the 2nd equation by 10:

35x + 10z = 335
30x + 10z = 300

Subtract 2nd equation from first:
5x = 35, so x=7, y=14, z=9.

2. John is not Romeo or Cleopatra, so he must be Anthony or Juliet.

Dan is not Juliet.
Karen went as Anthony, so John must be Juliet.
Beth is not Anthony or Cleopatra, or Juliet (because John is), so she is Romeo.

That means Dan must be Cleopatra, Beth is Romeo, John is Juliet, and Karen is Anthony.

Answer 4

n = 2q
n + q+d = 30
0.05n+0.1d+0.25q = 3.35
5n + 10d +25q = 335
10n + 10d + 10q +300
-5n +15q = 35
5n - 10q = 0
5q = 35
q = 7,...... (*.25 = 1.75)
n = 14,... (*0.05 = 0.70)
d = 9,....... (*0.1 = 0.90)
......................... $3.35

2)
Beth wore Romeo
John wore Juliet
Karen wore Anthony
Dan wore Cleopatra