Tom has some quarters (25c), dimes (10c), and nickels (5c). It is known that

Question

1. the total number of coins is 55;
2. the total value of the quarters equals the total value of the dimes and nickels
3. the number of dimes is three more than the sum of the numbers of quarters and nickles
4. How many quarters, dimes. and nickels does he have?

Answer 1

According to given information above we can set up equations as followings:

1) The total number of coins is 55;

Q + D + N = 55

2) The total value of the quarters equals the total value of the dimes and nickels

25Q= 10D + 5N

3) The number of dimes is three more than the sum of the numbers of quarters and nickles

D=Q+N+3 D - 3= Q +N

Using the equations above we can plug in D-3 for Q+N in the first equation:

D+ Q +N= 55

D+ (D-3)=55

2D - 3 = 55

2D = 55+3

2D= 58

D=29

If number of Dimes = 29 Then,

Q + N = 26

Q = 26 - N instead of number of quarters we can plug in (26- N) in the second equation:

25Q=10D+5N

25(26-N)=10*29 + 5N

650 - 25N=290 + 5N

650 - 290 = 25N + 5N

360= 30 N

360/ 30 = N

N=12

Since Q+N=26; Then Q+12 = 26 Q=26-12=14

Answer: Q=14, D=29, N=12

Answer 2

I agree with you David W. in all but this step:

14 + 26 + n = 55

n = 25

Q + D + N = 55

14 + 29 + N = 55

43 + N = 55

N = 55 - 43 = 12 nickels

14 + 29 + 12 = 55 ✔

and

0.25 * 14 = 3.50

29 * 0.10 + 12 * 0.05 = 2.90 + 0.60 = 3.50

3.50 = 3.50 ✔

I will 'fess up that finding the number of dimes was easy, but I had to take the slow way around to find quarters and nickels (comes from thinking too much like a programmer).

Teamwork makes the dream work!

Answer 3

25x+10y+5z

25x=10y+5z

x+y+z=55

y=55-x-z

z=55-y-x

x=55-y-z

y=3+x+z=55-x-z

2y=58

y=29

x+z=26

Need more imfo.

Answer 4

q + d + n = 55

25q = 10d + 5n ----> 5q = 2d + n

d = n + q + 3

Well, where to start?? Let's substitute the "value" of d into the 1st equaion.

q + n + q + 3 + n = 55

2q + 2n = 52

n + q = 26

Substitute 26 for n + q in the 3rd equation.

d = 26 + 3

d = 29

5q = 2(29) + n

5q = 58 + n

n = 5q - 58

29 = 5q - 58 + q + 3

29 = 6q - 55

84 = 6q

q = 14

14 + 26 + n = 55

n = 25

Check my answers!