Yvette has 5 more nickels than dimes. If the value of her money is $1.30, how many coins of each kind does she have?

- anonymous

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- anonymous

@gypsy1274 help me please?

- anonymous

Do you know how to solve systems of equations?

- anonymous

Yes I do

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## More answers

- anonymous

@gypsy1274

- anonymous

No need to tag me, after I post a response, I will get a notification whenever another response is posted.
nickels + dimes = 1.30
The second equation will need to include the values of those coins. Give it a try.

- anonymous

I'm still a bit confused on this so far I got $1.05

- anonymous

Umm @gypsy1274 ?

- anonymous

What is $1.05? What was the second equation?

- anonymous

Well I did $0.25+x=$1.50

- anonymous

Brain went dead....rebooting.....

- anonymous

☺

- anonymous

My train of thought derailed, let me get it back on track.....

- anonymous

Yvette has 5 more nickels than dimes. If the value of her money is $1.30, how many coins of each kind does she have?
\(n=d+5\) because there are five more nickels than dimes.

- anonymous

\(0.05n+0.10d=1.30\) because the value of the nickels plus dimes equals $1.30
Train is back on the rails now, sorry for the delay folks....

- anonymous

It's fine I guess I just want to figure this problem out because I have more HW to do for other classes

- anonymous

Do you understand these equations and where they came from? I'm sure they are correct this time, just verified it.

- anonymous

Since it says "5 more nickels" doesn't that mean it'll be 0.25 because your adding all the dimes together?

- anonymous

5 nickels are $0.25, that's true, but in that sentence, they are talking about the number of the coins not the values. The number of nickels equals the number of dimes plus five.

- anonymous

How do I know what to plug in in n and d ?

- anonymous

You don't plug in, you solve for them.
\(n=d+5\) is already solved for n so plug \(d+5\) in for n in the other equation:
\(0.5n+0.1d=1.30 \implies 0.5(d+5)+0.1d=1.30\)

- anonymous

I know you're trying to help me but your explaining it very good

- anonymous

I mean your not explaining it good my bad lol

- anonymous

@DebbieG - Perhaps you can try?

- anonymous

@e.mccormick I'm confusing this poor student, maybe you could help clarify?

- anonymous

@gypsy1274 thanks for trying though(: I appreciate it

- e.mccormick

Yah, I would do it with one equation. You have Dimes x and nickles x+5. Then, when you add those up with the proper value assigned you get 1.3.

- anonymous

What do you mean "add those up with the proper value"?

- e.mccormick

A dime is not just a word. It is a decimal value. =)

- e.mccormick

There is no reason for n or d because those have values. There is a count relationship between them. That count is a variable. So there are x dimes and x+5 nickles.

- anonymous

It still doesn't make much sence, my bad

- e.mccormick

If I said I had 72 dimes, you would instanly know I had $7.20. Right?

- anonymous

Yes

- e.mccormick

But why would you know?

- anonymous

Bc if I multiply 0.72 and 10 I get 7.20

- e.mccormick

Why .72? I had 72, not 72% of a dime.

- anonymous

Bc 72 dimes is written like that in decimal point

- e.mccormick

Yes. A dime is ten cents, or $0.10, and 72\(\times\)$0.10.
Similarly, a nickle is five cents or $0.05.
All I am saying is use that knowledge in the setup of the problem.

- anonymous

Would it be 0.10(5)+d=1.30

- e.mccormick

Not sure how you got there, but it is progress! That is one equation with one unknown, which is great. It is just not the right equation.

- e.mccormick

If I try and find d dimes and n nickles, I have to do two equations in two unknowns. But, if I restate the question this way:
Yvette has 5 more $0.05 than $0.10. If the value of her money is $1.30, how many coins of each kind does she have?
Can you do it in one unknown?

- anonymous

Ughhhhhhh!!!

- anonymous

I honestly have no clue right ow I have more HW to do still

- e.mccormick

As I said before, the dimes is the unknown. That means $0.10x must be part of this.

- anonymous

0.10(5)

- e.mccormick

I already gave you the dimes part. 0.10x. You need the nickles part.

- e.mccormick

How many nickles does it say she has? How would you write that if the number of dimes in the unknown?

- anonymous

$0.10x+$0.05y=$1.30

- e.mccormick

The problem with that is that it has two variables. So you need to get y in terms of x using a second formula. If x is the number of dimes, what is y in terms of x?

- anonymous

The number of nickels

- e.mccormick

That is y in terms of y. You need y in terms of x. Here is a huge clue. Take the first sentence. Replace dimes with x and nickles with y.

- anonymous

$0.05x+$0.10y=$1.50

- e.mccormick

That is completely wrong. Stick with $0.10x+$0.05y=$1.30. It is correct. But you need a second equation.
Yvette has 5 more nickels than dimes.
Yvette has 5 more y than x.
What is that line, and JUST that line, as a mathematical formula?

- anonymous

An equation ill say

- e.mccormick

Let me go completely sideways for a second to show an example using similar language.
If I have three pears and four apples, I have seven fruit. So:
3p+4a=7f.
But what if I said it differently?
I have one more apples than pears, and I have three pears. Then:
?a = 3p+1
The critical part is:
a=p+1
Saying some more this than that means: that = this + some.

- anonymous

$0.05+0.10x=$1.30 ?

- e.mccormick

The $1.30 is not involved in the second equation. Just x, y, and some number creating a relationship between x and y. x being the number of dimes, y being the number of nickles, and the line: Yvette has 5 more nickels than dimes. Telling you all you need to know about that relationship.

- e.mccormick

They give you four numbers in this equation:
Nickle, AKA:$0.05
Dime, AKA: $0.10
Total $1.30
and 5.
You took it with two unknowns, number of nickles y and number of dimes x. OK.
To do two equations, they must both use x and y. However, the goal is to break up the rest of the information. The first equation you did is fine.
$0.10x+$0.05y=$1.30
It uses both x and y as required. It also uses $0.10, $0.05, and $1.30. Therefore your second equation can NOT use those or it is not generating new information. That leaves you with an equation involving: x, y, and 5. They tell you how to use 5 when they say:
Yvette has 5 more nickels than dimes.
So what is the equation?

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