Question

Ivan has nickels and dimes in his pocket. The total number of nickels and dimes is 16. The total value of the coins is $1.25. How many of each coin does he have?
A. 6 nickels and 10 dimes
B. 7 nickels and 9 dimes
C. 8 nickels and 8 dimes
D. 9 nickels and 7 dimes

Answer 1

A nickel is worth 0.05 and a dime is worth 0.10, you need a total of 1.25
to set up the equation, you would say
0.05N+0.10D=1.25

Answer 2

and to set up the equation for simply the number of coins is
n+d=16

Answer 3

There are two ways to solve this, would you like to use elimination or substitution?

Answer 4

elimination

Answer 5

ok, To solve by elimination, we need to figure out which variable you would like to eliminate.

Answer 6

Would you like to eliminate the D or N?

Answer 7

d

Answer 8

Ok. So at the moment this is how both our equations look together.
0.05N+0.10D=1.25
N+ D=16

Answer 9

Here's a trick I like to do because I don't like decimals all that much.

Answer 10

Because I want to get rid of the decimal, and the decimal makes the numbers fall into the hundreths place, I move the decimal over to the right 2 spots. This makes the equation turn from
0.05N+0.10D=1.25
to
5N+10D=125

I only do this to equations with decimals.

Answer 11

So now our two equations are
5N+10D=125
N+ D=16

Now, you chose to eliminate the D's.
In order to eliminate the D's completely, they need to be the opposite sign and same number.
Lets do that.
we need 10D to be the opposite sign=> so we will multiply D by a (-1), and the same number so we also multiply by (10)
Meaning we multiply the D in the second equation by (-10)
but if we do something to one term in the equation, it has to be done to all.
So we do this:
N+D=16
(N+D=16)(-10)
This becomes
-10N-10D=-160

So now the equations together look like this:
5N+10D=125
-10N-10D=-160

Questions so far?

Answer 12

No thank you for spending the time to help me with this

Answer 13

My question would be A. wouldn't it.

Answer 14

No problem!
ok so from there, we add the equations, watch out for those negatives! I want you to try and solve this, only solve up to the part where you eliminate the D's, then type out your equation. We will go from there!
( 5N+10D=125 )
+(-10N-10D=-160)
-----------------

Answer 15

A is wrong

Answer 16

I've done thanks to you! i have my problem thank you for helping me i just got a 100% i needed help with that problem.

Answer 17

You understood it all? Ya sure? We haven't finished hahaha.