Question

A piggy bank contains 50 coins, all of them nickels, dimes, or quarters. The total value of the coins is $5.60, and the value of the dimes is five times the value of the nickels. How many coins of each type are there?
a. write the system of equations
b.Set up a matrix equation AX=B and solve it.

Answer 1

x+y+z = 50

x(.05) + 5x(.05) +z(.25) = 5.60

Does this sound right?

Answer 2

yes

Answer 3

.05x +.25x +.25z = 5.60
30x +25z = 560
x = (560 - 25z) - 30

getting warmer?

Answer 4

its hard to set up a matrix in here :)

Answer 5

yes thank you

Answer 6

typo:

x = (560 - 25z)/30 is correct

Answer 7

we can simplify this by factoring out 5 from everything:

x = (112 - 5z)/6

Answer 8

Ok

Answer 9

z = 50-x-y

and y = 5x so

z=50-x-5x

z = 50 -6x

Answer 10

my professor wants us to put it into a matrix box, and we're supposed to use a calculator to find the inverse, and the multiply it to get the answer. it's supposed to be a 3 x 3 matrix in the calculator, then multiply it by a 1 x 3 matrix

Answer 11

we briefed over matrix in class, so I aint to knowledgeable about them. Just what I taught meself

Answer 12

ok thanks anyway

Answer 13

I was talking with myself last night, I said self? how can we solve this problem using Georgia Math. Myself replied, by using canadian money :)

How many quarters are in 5.60? at most 22 barring any restrictions like nickels and dimes...

n + d + q = 50
---------------------------
1 5 (44) = q>22; no good
2 10 (38) = ''
3 15 (32) = "
4 20 (26) = "
5 25 (20) = maybe
6 30 (14) = maybe
7 35 (8) = maybe
8 40 (2) = maybe
9 45 (0) = to many coins..

Got it narrowed down. Now lets see which ones equal the illusive $5.60:

5 25 (20) = .25 + 2.50 + 5.00 = too much
6 30 (14) = .30 + 3.00 + 3.50 = "
7 35 (8) = .35 + 3.50 + 2.00 = "
8 40 (2) = .40 + 4.00 + .50 = 4.90 (not enough)

If I did my Georgia Math correctly, there is no "real" money in the piggy bank....

Answer 14

But then again, we figured on dimes being 5 times the number of nickels and not 5 times the value of the nickels.... back to the drawing board......

Answer 15

dimes can only be multiples of .10; which limits our nickels to increments of 2

n $ d$ d = n+d ($) q (odd = "x.x5")
---------------------------------
2 (.10) (0.50) 5 = 7 (0.60) 43 - odd bad
4 (.20) (1.00) 10 = 14 (1.20) 36 - (+9.00) bad
6 (.30) (1.50) 15 = 21 (1.80) 29 - odd bad
8 (.40) (2.00) 20 = 28 (2.40) 22 - (+4.50) bad
10 (.50) (2.50) 25 = 35 (3.00) 15 - odd bad
12 (.60) (3.00) 30 = 42 (3.60) 8 - (+2.00) GOOD!!
14 (.70) (3.50) 35 = 49 (4.20) 1 - odd bad
16 (.80) (4.00) 40 = 56>50 coins

After much deliberation and a majority vote of congress we come to the conclusion that the piggy bank holds:

12 nickels 30 dimes and 8 quarters.

And should be put into an interest bearing account at 4% compounded monthly for 50 years :)