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.