Math Homework.....Help!?

Question

I can't figure it out....
Jessica has 16 dimes and quarters. Whitney has twice as many dimes and 1/3 as many quarters as Jessica has. If they both have the same amount of money, what coins does each have?

Answer 1

Given:
16 = number of dimes and quarters Jessica has

If you let x = number of dimes Jessica has, then it follows that
the number of quarters she has is,
16 - x = number of quarters Jessica has

Now, according to the problem, Whitney has twice as many dimes as Jessica, so we can write this as
2x = number of dimes Whitney has.
Again, according to the problem, Whitney has 1/3 as many quarters as Jessica, so we can write this as,
1/3(16 - x) = number of quarters Whitney has

The problem says they both have the same amount of money.
This means we can set the amount of money of Jessica equal to the amount of money of Whitney.

10x +25(16 - x) = 10(2x) + 25[1/3(16 - x)], since
a dime is equal to 10 cents and a quarter is equal to 25
cents.
Solving:
10x +400 - 25x = 20x + 25[16/3 - x/3]
-15x + 400 = 20x + 25[(16 - x)/3]
- 15x - 20x = -400 + 25(16)/3 - 25(x)/3
Multiply left and right sides by LCD = 3:
3(-15X) -20x(3) = 3(-400) + 25(16) - 25x
-45x - 60x = -1200 + 400 - 25x
-45x - 60x + 25x = -800
-80x = -800
x = -800/-80


x = 10 dimes ANS. Jessica
16 - 10 = 6 quarters ANS. Jessica

For Whitney:
2(10) = 20 dimes ANS
1/3(16 - 10) = (1/3)(6) = 2 quarters ANS


teddy boy

Answer 2

Let d be the number of times Jessica has.
Let q be the number of quarters Jessica has.

So that means d + q =16

We also know that Whitney and Jessica have the same amount of money. Let the left side of the equation be Jessica's coins and the right side be Whitney's coins.

10d + 25q = 10 * 2d + 25 * q/3

Getting rid of fractions in the second equation:

30d + 75q = 60d + 25q

50q = 30d

d = 5/3 * q

Substitute that into the first equation:

5/3 * q + q = 16

8/3 q = 16

q = 6

So, Jessica has 6 quarters and 10 dimes.

Likewise, this means Whitney has 2 quarters and 20 times.

Both girls have $2.50 in coins.

Answer 3

Jessica has 6 quarters and ten dimes
Whitney has 20 dimes and 2 quarters

Answer 4

Jessica has 16 dimes and 16 quarters =
Whitney has 32 (16X2=32) dimes and 5.3 (16/3= 5.3) quarters. OH forget it that is why I went into a job that I don't have to do math. Sorry I tried.