I Need HELP( with a Word Problem)?

Question

Vivian has $4.05. all in quaters and dimes. She has twice as many dimes as quaters. How many of each coin does she have...
( Thank you so much I need the work and the Explanation)
Once agian THANK YOU SOOOOOOOOO MUCH!

Answer 1

Suppose Vivian has x quarters = 25x cents.
Then she has 2x dimes = 20x cents.
$4.05 = 405 cents.

Therefore:
20x + 25x = 405
(20 + 25)x = 405
45x = 405
Divide by 45:
x = 405 / 45
x = 9.

Vivian therefore has 9 quarters and 18 dimes.

Answer 2

That's a Math problem. If you post Math questions there, you'll probably get more answers. But here's how to look at that--start making guesses, starting with the number of quarters. You know automatically that she is going to have to have an odd number of quarters, because she has only five cents after an even amount. So, what if you start with 7 quarters? Then she has how much money? Do that math. She has $1.75. Now then, take 14 dimes, which is double the amount of quarters. That gives you $1.40. Does 1.75 + 1.40 equal 4.05? No. So now jump up to your next odd number of quarters, 9. What is 9 x 25? Then if you have 9 quarters, you would have 18 dimes. What is 18 x 10? Add those together. Got it?

Answer 3

These problems are usually easier if you do them in terms of pennies rather than dollars so you don't have decimals.

Choose variables to represent the number of quarters (Q is a good one) and dimes (D) that Vivan has.

The value of each quarter is 25, so the total value of all her quarters is 25Q. The value of each dime is 10, so the total value of all her dimes is 10D. The total value of all her coins is 405 = Quarters plus Dimes is 405. This English sentence translates into the Mathematical sentence (equation)

25Q + 10D = 405

"She has twice as many dimes as quarters" can be reworded to say "the number of dimes is 2 times the number of quarters." This translates into the math equation

D = 2Q

Now since D is the same as 2Q (that's was D=2Q means), you can go back to the first equation and replace every D with a 2Q

25Q + 10 (2Q) = 405.

Solve this for Q. Use your Q to figure out D.

Answer 4

Let x = number of quarters

then 2x = number of dimes

Here is where we need to be careful, setting up the equation

The value of the quarter is 0.25x
while the value of the dimes is 0.10x
but we had twice as many dimes as quarters.

0.25x + 0.10 (2x) = 4.05

0.45x = 4.05

x = 9 (number of quarters)

2x = 18 (number of dimes).
.

Answer 5

Trial and error.

9 quarters and 18 dimes.

Answer 6

Q=quarters=25
D=dimes=10
X= number of quarters
so 2x = number of dimes

now we know
2XD+XQ=4.05
2X*10+X*25=4.05
simplify for x and you find x = 9

Answer 7

9 quarters $2.25
18 dimes $1.80
******
$4.05

Answer 8

figure it out it is not that hard.