Question

help needed!!!!!!!1
JUSTIN BEIBER has 9.68 in his pocket , made of nickels and pennies . he has 248 in total how many of each?

Answer 1

how would you arrange the equasion with this set of data?

Answer 2

You would have two equations... one that relates the # of coins he has and one that relates the total value of the coins.
You can let "p = # of pennies" and "n = # of nickels" and then use expressions like "0.01p" to represent the value of the # of penies you have, since if you have 5 pennies, the expression is "0.01*5" or "0.05."

Answer 3

so one would be 9.68=n+p
where n is the number of nickels and p, pennies?

Answer 4

the other 248=n+p?
is that right?

Answer 5

9.68 is the total value of the coins. This equation would be the one to use 0.01p and 0.05n in.
9.68 = 0.01p + 0.05n

That equation basically represents the sum of the values of your pennies and nickels. The other one is correct.

Answer 6

0.01p + 0.05n = 9.68
p + n = 248

You can multiply the entire first equation by -100 to get integers without decimals and then solve by elimination because the -p and p will cancel.
-p - 5n = -968
p + n = 248

Answer 7

why would you multiply it by -100?

Answer 8

is it to convert to $ ?

Answer 9

the *100 would get rid of the decimals in the equation. I prefer to do this because its typically easier to work with integers than decimals. The reason I use a negative is because I want to solve by elimination, so I want my first equation to have a value we can eliminate, the -p.

It's not necessarily the only way you can solve it.... you could solve for a variable in the second equation and substitute also.

Answer 10

could you help me do it the easiest and simplest way ? ; im new to this stuff

Answer 11

0.01p + 0.05n = 9.68
p + n = 248

p = 248 - n Subtract off n to solve for p

0.01(248 - n) + 0.05n = 9.68 Substitute p=248-n
2.48 - 0.01n + 0.05n = 9.68 Add like terms
2.48 + 0.04n = 9.68 Subtract 2.48 from both sides
0.04n = 7.2 Divide by 0.04.
n = 180

p = 248 - 180 Put n back into p=248-n
p = 68

Answer 12

My first method looks like this:

0.01p + 0.05n = 9.68
p + n = 248

-p - 5n = -968
p + n = 248 Add together parts of the equations
--------------
-4n = -720
n = 180

p + 180 = 248 Back-substitute n=180 into second equation
p = 68

Answer 13

I used \(p = 248 - n\) to get the first equation to have only one-variable. This allowed me to solve for n.

If you're confused as to why I 'could' do that, just consider that we can add and subtract things to both sides of the equation and still have equivalent expressions. We can also multiply and divide both sides by constants and still have equivalent expressions.
\(p + n = 248\) is true, given by the problem. If we subtract \(n\) from both sides, it's still true as long as we subtract from both sides.

\(p + n - n = 248 - n \implies p = 248 - n\)

Then, since it would be true that \(p\) does equal that, we can subtitute that value back into the other equation to still have a true value.

\( 0.01p + 0.05n = 9.68~~~\text{substitute} p = 248-n\\\implies 0.01(248 - n) + 0.05n = 9.68\)

Answer 14

i got it but since im dum your last line confused me

Answer 15

basically, we take the value that p = and put that in p's place.