# Thread: Help me find the third equation in this systems of equations problem.

1. ## Help me find the third equation in this systems of equations problem.

This problem has annoyed me to no end considering it was assigned to my sister who is in Algebra 2. And here I am, in Calculus, and I cannot for the life of me figure it out by any method other that guess and check. I know that it is a systems of equations problem with 3 variables which requires 3 equations to work the system. Problem is, all I can pull from the problem is 2 equations.

Here's the word problem:
A boy went to a candy store and spent exactly one dollar on exactly 100 pieces of candy. He bought some at 5 cents, 2 cents, and 10 for a penny. How many of each kind did he buy?

Here's what I've got so far:
.001x + .02y + .05z = 1
x + y + z = 100

I think the third has something to do with the 10 for a penny. Something to the order of only buying in increments of 10.

Any ideas?

2. Originally Posted by havokblue
This problem has annoyed me to no end considering it was assigned to my sister who is in Algebra 2. And here I am, in Calculus, and I cannot for the life of me figure it out by any method other that guess and check. I know that it is a systems of equations problem with 3 variables which requires 3 equations to work the system. Problem is, all I can pull from the problem is 2 equations.

Here's the word problem:
A boy went to a candy store and spent exactly one dollar on exactly 100 pieces of candy. He bought some at 5 cents, 2 cents, and 10 for a penny. How many of each kind did he buy?

Here's what I've got so far:
.01x + .02y + .05z = 1
x + y + z = 100

I think the third has something to do with the 10 for a penny. Something to the order of only buying in increments of 10.

Any ideas?
Equation 1 is wrong.

If he bought 10 of lolly $\displaystyle x$ for a penny, then surely

$\displaystyle 10x = \$0.01\displaystyle x = \$0.001$.

Therefore

$\displaystyle 0.001x + 0.02y + 0.05z = 1$

$\displaystyle x + y + z = 100$.

But you already know that he bought 10 of lolly $\displaystyle x$, so $\displaystyle x = 10$.

Therefore

$\displaystyle 0.001\cdot 10 + 0.02y + 0.05z = 1$

$\displaystyle 10 + y + z = 900$

$\displaystyle 0.02y + 0.05z = 0.99$

$\displaystyle y + z = 90$.

Can you go from here?

3. Oh, sorry that was a typo. Thanks for pointing that out.

You can't simply work it like that. I didn't understand this either when I saw the problem at first. He doesn't JUST buy 10 at .01.
He buys in SETS of 10. The actual answer has him buying 7 sets of 10 at .01.

4. Originally Posted by havokblue
Oh, sorry that was a typo. Thanks for pointing that out.

You can't simply work it like that. I didn't understand this either when I saw the problem at first. He doesn't JUST buy 10 at .01.
He buys in SETS of 10. The actual answer has him buying 7 sets of 10 at .01.
That's not how the question reads, but in that case, I can only see 2 equations in three unknowns as well.

If you have the answer using trial and error, just use the trial and error answer.

5. I really think she copied the problem down incorrectly and there's information missing. It's insane for them to have to solve a three variable system by guess and check alone.