Tim has 28 coins made up of nickels, dimes and quarter. He has four more dimes than nickels and quarters combi

Question

Tim has 28 coins made up of nickels, dimes and quarter. He has four more dimes than nickels and quarters combined. How many each kind of coin does he have if their toal value is $ 3.20.

Answer 1

The problem states

1) n + d + q =28,

2) d + 4 = n + q, and

3) 5n + 10d + 25q = 320 == (divide everything by 5)

4) n + 2d + 5q = 64

Solving for d in the first 2,

d = 28 - n - q and

d = n + q - 4; adding the 2 equations we have

2d = 28 - 4 + n + q - n - q ==

2d = 24 ==

d = 12 = the number of dimes. Substituting 12 for d in 2) & 4),

12 + 4 = n + q ==

5) n + q = 16 and

n + 2(12) + 5q = 64 ==

6) n + 5q = 40

Subtracting 5) from 6) we have

[n + 5q = 40] - [ n + q = 16] ==

4q = 24 ==

q = 6 = number of quarters. Substituting 6 for q and 12 for d in 1),

n + 12 + 6 = 28 ==

n = 10 = number of nickels

Answer 2

N + D + Q = 28 N + (N+Q+4) + Q= 28; 2N + 2Q = 28 5N + 10D + 25Q= 320 Solving these simultaneously gives: 7 nickels, 16 dimes, 5 quarters.

Answer 3

D = number of dimes
N = number of nickels
Q = number of quarters

There are 4 more dimes than nickels and quarters combined:
D = N + Q + 4

There are a total of 28 coins:
D + N + Q = 28 or 2(N + Q) = 24 and N + Q = 12
So there are 16 dimes (28 - 12 or 12 + 4)

The total value of all coins is 3.20:
.10D + .05N + .25Q = 3.20
1.60 + .05N + .25Q = 3.20
.05N + .25Q = 1.60

.05N + .25Q = 1.60
N + Q = 12 and .05N + .05Q = .6
.25Q - .05Q = 1.60 - 0.6
.20Q = 1.0
And Q = 5
Since N + Q = 12 this means N = 7

There are 7 nickels, 16 dimes and 5 quarters

Check:
7*.05 + 16*0.1 + 5*.25 = 3.20

Answer 4

I'd say you have 3 unknown quantities and 3 equations:

1. The total number of nickels, dimes and quarters is 28.
2. Nickels+quarters = dimes-4.
3. Total value (1 nickel = 0.05, 1 dime...) = 3.20$.

Either use linear algebra to solve the matrix or just isolate some variables and plug them into the other equations.

Answer 5

quarter 8 0.914285714
nickels 8 0.914285714
dimes 12 1.371428571
total 3.2

To get the numbers we have 28 less 4. to get the number that equals them that is 20.
Divided it by three (20/3) to get 8 for each then for one add 4 to get the value of dimes to be 12.
Dimes 12
Nickels 8
Quarter 8
Total 28

Answer 6

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

x + y + z = 28
x = y + z + 4
x = (28 - x) + 4 = 32 - x
2x = 32
x = 16
y + z = 12
0.1x + 0.25y + 0.05z = 3.2
1.6 + 0.05(5y + z) = 3.2
0.05 (5y + z) = 1.6
Now
5y + z = 1.6/0.05 = 32
y + z = 12
subtracting: ` ` ` 4y = 20
y = 5
z = 7

Ans: 7 nickels, 16 dimes, 5 quarters