math help?

Question

Justine has some rare quaters and nickels. She has 8 more nickels than quaters. The face value of the coins is $2.50. How many are quaters?


Please tell me how you got your answer.

Answer 1

Set up equations with the info given. Let quarters be Q and nickels be N.

8 more nickels than quarters means N = Q + 8

For the total value, .05 times the number of nickels (N) + .25 times the number of quarters (Q) would give you the total value (which is given as $2.50)

So .05N + .25Q = 2.50

You can substitute Q+8 for N and get

.05(Q+8) + .25Q = 2.50

.05Q + .40 + .25Q = 2.50
.30Q + .40 = 2.50
.30Q = 2.10
Q = 7

There are 7 quarters.

Just to make sure, let's check. If there are 7 quarters, and eight more nickels than quarters, then there must be 15 nickels. 7 quarters is $1.75 and 15 nickels is $.75. $1.75 + $.75 = $2.50, so the answer holds up.

Answer 2

The are 7 quaters and 15 nickels. 15-7=8

Answer 3

Let q = how many quarters. Then q+8 = how many nickels.

q quarters are worth 25q cents; (q+8) nickels are worth 5(q+8) or 5q+40 cents.

Add together to get 250 cents: 25q + 5q + 40 = 250

That's 30q + 40 = 250, or 30q = 210

So q = 7 because that's what 210/30 is. Then q+8=15.

Check: 25x7 + 5x15 = 175+75=250 check

Answer 4

Let x be the number of nickels.
Then 5x = the total value of nickels (in pennies).

Let y be the number of quarters.
Then 25y = the total value of the quarters.

Our equations are:
x = y + 8
5x + 25y = 250

Since x = y + 8, we can rewrite the second equation as:
5*(y+8) + 25y = 250
30y = 210
y = 7

And since x = y+8, it follows that x = 15

Justine has 15 nickels and 7 quarters.

Answer 5

n= number of nickels and q= number of quarters, n(.05) + q(.25) = 2.5, also q + 8 = n, so you, since you've solved for one variable you take that and subsitute it into the other equation, (q+8)(.05) + q(.25) = 2.5, now solve for q, the equation becomes (.05q + .4) + .25q = 2.5, subtract the .4 and u get .05q + .25q = 2.1, factor out a q and you get q(.05 + .25)=.21, add and then divide and you get q=7, and thats your answer, you can check to see if it works by substiting in 7 for q

Answer 6

25x + 5(x + 8) = 250
5x + (x +8) = 50
6x + 8 = 50
6x = 42
x = 7 quarters 15 nickel

Answer 7

Let quaters =x
Nickles = x +8
x(0.25)+(x+8)(0.05) = 2.50
25 x + 5x +40 =250
30x =210
x =7

Answer 8

she has 7 quarters and 15 nickels
seven quarters = 7*0.25 = $ 1.75
fifteen nickels = 15*0.05= $ 0.75
total money = $2.50

Answer 9

Let's use x to = # of quarters. Then:
x(.25) + (x+8)(.05) = 2.50
.25x + .05x + .40 = 2.50
.30x = 2.10
x = 7 = # of quarters, then
x + 8 = 15 = # of nickels.
Check:
7 x .25 = 1.75
15 x .05 = .75
1.75 + .75 = 2.50

Answer 10

n = q + 8

.05n + .25q = 2.50
5n + 25q = 250
5(n + 5q) = 250
n + 5q = 50

(q + 8) + 5q = 50
q + 8 + 5q = 50
6q + 8 = 50
6q = 42
q = 7

n = 7 + 8 = 15

15 nickles
7 quarters