Applied verbal problems [Solved!]

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.

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?

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?

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

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!

X

No problems,
Regards