solving system of equations

Question

suppose you have 12 coins that total $.32. Some of the coins are nickels and the rest are pennies. how many of each do you have?

Answer 1

Melissa

 

Let x = the number of nickels

and y = the number of pennies

 

Thus,

 

x+y=12 total number of coins

 

0.05x+0.01y=0.32

 

To simplify this problem, I would multiply the second equation by 100 in which becomes

 

5x+y=32

 

Now you could use elimination to solve the system of equations in which y is the easiest to eliminate by simply subtracting the second equation from the first in which is:

 

x-5x+y-y=12-32 This implies -4x=-20 Hence, x = 5. Just substitute x=5 into one of the equations to solve for y.

Answer 2

Hi Melissa,

 

Answer is 5 nickels and 7 pennies.  Here is how I got it.

 

5n + 1p = 32

 

Since the amount ends with 2, amount of pennies must be end with either 2 or 7 because nickels always end with 0 or 5 (0+2 or 5+7 to make last number 2).

 

First, let's try 6 nickels & 2 pennies to make 32 cents.  It doesn't work because it only gives you 8 coins.

 

Second, let's try 5 nickels & 7 pennies to make 32 cents.  It works: (5x5 + 1x7    25+7 = 32).  And5+7 = 12!!!

 

So "you" have 5 nickels and 7 pennies.

 

Good luck to you.