help with a word problem?

Question

please help w/ following word problem:

Maria has 11 more nickels than quarters. The total of nickels and quarters are $15.85
How many of each does she have?

Answer 1

so x will represent the amount of quarters you have

so you can make the equation

(x+11)(.05) + (.25) (x) = 15.85
0.05x + .55 + .25x = 15.85
.3x + .55 = 15.85
.3x = 15.3
x = 51

so if x = 51, than you have 51 quarters
and x + 11 = 51 + 11 = 62
so you have 62 nickels!

Answer 2

Let's call the number of quarters Q, which would make the number of nickels Q+11. Then we form an equation relating the values of the coins to the total value of $15.85.:

.05(Q+11) + .25Q = 15.85

You can move each decimal place two places to the right (multiplying by 100):

5(Q+11) + 25Q = 1585
5Q + 55 + 25Q = 1585
30Q = 1530
Q = 51 = # of quarters
therefore # of nickels = Q+11 = 51+11 = 62

Answer 3

n = number of nickels
q = number of quarters

q+11=n
25q + 5n = 1585 Divide each term by 5
5q + n = 317 Rearrange first equation into this order.
q-n=-11 Add these two equations together.
6q=306
q=51 She has 51 quarters.
q+11=51+11=62 She has 62 nickels.

Check
51 quarters = 51*25= 1275 cents
62 nickels = 62*5=310 cents
1275+310=1585 cents = $15.85 Correct

Answer 4

If we take total no. of quarters to be X, then nickels would be X+11

value of quarters = X x $0.25
Value of nickels = (X+11) x 0.05

so 0.25X + 0.05X + 0.55 = 15.85
0.3X = 15.85 - 0.55
0.3X = 15.3
X = 51

so quarters = 51
nickel = 51 + 11 = 62

Answer 5

let q be the number of quaters
and n be the number of nickels

n = q + 11

we know nickels worth .05
and quarter worth .25

.25q + .05n = 15.85

.25q + .05(q +11) = 15.85
.25q + .05q + .55 = 15.85
.3q = 15.3
q = 51

so there are 51 quaters and 62 nickels

Answer 6

Let's say nickels=n and quarters=q.
Start with a system of equations derived from the problem.
.05n+.25q=15.85 and
q+11=n

Since one equation has an isolated n value, you can substitute it into the other equation.
.05(q+11)+.25q=15.85
.05q+.55+.25q=15.85
.55+.30q=15.85
.30q=15.30

Dividing 15.30 by .30, we find the value of q to be 51. Now we substitute 51 into one of the original equations.
q+11=n
51+11=n
62=n

So Maria has 51 quarters and 62 nickels.

To check, substitute both values into the other original equation:
.05n+.25q=15.85
.05(62)+.25(51)=15.85
3.10+12.75=15.85
15.85=15.85
It checks.

Answer 7

51 quarters, 62 nickels.

Answer 8

Let x = number of quarters
Then x+11 = number of nickles
So .25x +.05(x+11) = 15.85
.25x +.05x +.55 =15.85
.3x = 15.3
x= 51 = number of quarters
x+11 = 62 = number of nickles