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.