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Applied verbal problems [Solved!]

My question

Can you help me with this Verbal Problem and show me the equation(s) I could use to solve it.

Evan has seventy bills, in an assortment of ones, fives, and tens totaling $100. How many bills of eack kind does he have.

Any help is appreciated

Relevant page

6. Applied Verbal Problems

What I've done so far

I went through your examples of Verbal Problems but I'm still at a loss to set this up. I figured of the answer but it's bugging me I can't get the equation.

X

Can you help me with this Verbal Problem and show me the equation(s) I could use to solve it.

Evan has seventy bills, in an assortment of ones, fives, and tens totaling $100. How many bills of eack kind does he have.


Any help is appreciated
Relevant page

<a href="/basic-algebra/6-applied-verbal-problems.php">6. Applied Verbal Problems</a>

What I've done so far

I went through your examples of Verbal Problems but I'm still at a loss to set this up.  I figured of the answer but it's bugging me I can't get the equation.

Re: Applied verbal problems

Hello Verna

Hmmm - your problem is a bit more involved than any on that page you came from.

To get you started, you could set up something like:

Let A be the number of $1 notes
Let B be the number of $5 notes
Let C be the number of $10 notes.

From the question, what is `A + B + C = ?`

And from the question, what $ value has `A + 5B + 10C = ?`

Now, we have got 3 unknowns, but only 2 equations. But you can eliminate one of the variables by subtracting one of the equations from the other (I suggest subtract first from second, so you have positive numbers.)

Can you go from there?

X

Hello Verna

Hmmm - your problem is a bit more involved than any on that page you came from.

To get you started, you could set up something like:

Let A be the number of $1 notes
Let B be the number of $5 notes
Let C be the number of $10 notes.

From the question, what is `A + B + C = ?`

And from the question, what $ value has `A + 5B + 10C = ?`

Now, we have got 3 unknowns, but only 2 equations. But you can eliminate one of the variables by subtracting one of the equations from the other (I suggest subtract first from second, so you have positive numbers.)

Can you go from there?

Re: Applied verbal problems

Well, `A+B+C = 70` (number of bills)

`A + 5B + 10C = 100` (total amount of money)

Subtracting:

`A + 5B + 10C = 100`
`A+B+C = 70`

`4B + 9C = 30`

Is that correct? I'm stuck now - what to do?

X

Well, `A+B+C = 70` (number of bills)

`A + 5B + 10C = 100` (total amount of money)

Subtracting: 

`A + 5B + 10C = 100`
`A+B+C = 70`

`4B + 9C = 30`

Is that correct? I'm stuck now - what to do?

Re: Applied verbal problems

Now we are left with one equation with 2 variables. How to solve it? Well, the other constraint in this problem is that `A, B` and `C` must be whole numbers.

So some trial and error quickly helps us find the right combination.

For example, if I put `B = 1`, then it turns out that `C = 26/9`, which is not a whole number. Try a few more values of `B` and you can get a whole number value for `C`. Then work backwards with your `B` and `C` values to get the `A` value, based on what the question tells you.

Regards

X

Now we are left with one equation with 2 variables. How to solve it? Well, the other constraint in this problem is that `A, B` and `C` must be whole numbers.

So some trial and error quickly helps us find the right combination.

For example, if I put `B = 1`, then it turns out that `C = 26/9`, which is not a whole number. Try a few more values of `B` and you can get a whole number value for `C`. Then work backwards with your `B` and `C` values to get the `A` value, based on what the question tells you.

Regards

Re: Applied verbal problems

`B=2` didn't work, but `B=3` gives `C=2`.

Then `A=65`.

Testing what I got:

`A+B+C=65+3+2=70`

`A+5B+10C=65+15+20=100`

It works! Thanks so much!

X

`B=2` didn't work, but `B=3` gives `C=2`.

Then `A=65`.

Testing what I got:

`A+B+C=65+3+2=70`

`A+5B+10C=65+15+20=100`

It works! Thanks so much!

Re: Applied verbal problems

No problems,
Regards

X

No problems,
Regards

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