Question

For this question, you will need a friend. (me myself and i) Have this individual grab a handful of coins making sure there are only two types of coins in the group (i.e., nickels and dimes, quarters and pennies, pennies and dimes, etc). Your friend should tell you the type of coins they’ve chosen, how many coins they have and the dollar amount of the group. From this information, you will set up two sets of equations and determine how many of each coin they have in their hand.

Answer 1

I have 17 coins.

Answer 2

12 pennys and 5 quarters

Answer 3

The value is $1.37.

Answer 4

I dont know how to set up the two equations

Answer 5

\[p + q = 17 ~~ \text{and} ~~ p + 0.25q = 1.37\]

Answer 6

Just assume your friend grabbed 17 coins (quarters and pennies) and the total value was $1.61.

Your first equation describes how many coins are being held:

x + y = 17

The second equation describes how much the group is worth

25x + 1y = 161

X is your quarters and Y is your pennies.

Now solve the system of equations.

25x + y = 161
x + y = 17

Get rid of the y's by multiplying the left and right side of the second equation by negative 1 and then adding the equations together:

25x + y = 161
-1 * ( x + y = 17 )

Gives you

25x + y = 161
-x - y = -17

Combining these equations gives you

24x = 144

Solve for x and you get 6.

Now plug 6 in for x in your original x + y = 17 equation

6 + y = 17
y = 11

So your friend had 6 quarters and 11 pennies.

Answer 7

thank you