a math question?

Question

a coin bank contains $12.75 in nickels,dimes,and quarters.There are twice as many dimes as nickels and 3 fewer quarters than dimes. How many of each type of coin are there

Answer 1

Answer:
18 nickels
36 dimes
33 quarters

Explanation:
x = # of nickels
2x = # of dimes
2x-3 = # of quarters

Now multiply each # of coins, in terms of x, by the amount each is worth (ex: a nickel is worth 5 cents so if there are x nickels then there is .05x amount of money in nickels) and set the whole thing equal to your total which is $12.75:

x(.05) + 2x(.10) + .25(2x-3) = 12.75
.05x + .2x + .5x - .75 = 12.75
.75x - .75 = 12.75
.75x =13.50
x = 18

So...
# of nickels = 18
# of dimes = 2x = 36
# of quarters = 2x-3 = 33

Answer 2

D=2N Where D is dimes and N is nickels.
Q= D-3 where Q is quarters and D is dimes.

Think of 12.75 as a lot of pennies. Each N is worth 5 pennies, D is 10 pennies, and Q is 25, so
25Q +10D + 5N = 1275 (divide both sides by 5)
5Q + 2D + N =255 You now have 3 unknowns and 3 equations so you can start substituting.
Remember, D =2N and Q =D-3 or 2N-3
So 5Q + 2D + N = 255 can be rewritten with just N's.
5(2N-3) + 2(2N) + N = 255
10N-15 + 4N + N =255
15N -15 = 255 Add 15 to both sides
15N = 270 Divide both sides by 15
N= 18 nickels So D = 2N =36 dimes and Q = D-3 or 33 quarters Be sure to check it.

Answer 3

5 nickels*.05 cents
.25 cents
5*2 because there are twice as many dimes as nickels equals
10
10 * $ .1 cent
$1
10-3 because there are 3 less quarter than dimes
is 7
7*$.25 cents
$1.75
$1.75+$1+$.25
$3
So, the answer is that there are 5 nickels, 10 dimes, and 7 quarters

Answer 4

You need three equations - one for the monetary value of the money and two for the number of coins.

Three variables, N = numberof nickles, D = number of dimes and Q = number of Quaters

.05N + (.10)D +.25Q = 12.75

Twice as many dimes as nickles

2N = D and

D-3 = Q

Solve for the variables - Do not want to do all of the work.

Answer 5

x = number of nickels
y = number of dimes
z = number of quarters

.05x + .10y + .25z = 12.75
y = 2x -> x = .5y
z = y - 3

Plug in: .05(.5y) + .10y + .25(y-3) = 12.75

And solve from there.

.025y + .10y + .25y = 13.50

.375y = 13.50
y = 36 -> z = 33 -> x = 18

18 nickels, 36 dimes, 33 quarters