Question 709813: a vending machine accepts nickels, dimes, and quarters. exact change is needed to make a purchase. how many ways can a person with four nickels, three dimes, and two quarters make a 65-cent purchase from the machine?
Found 2 solutions by josgarithmetic, Edwin McCravy:
Answer by josgarithmetic(39620)   (Show Source):
You can put this solution on YOUR website! This is really a Counting Principles problem. Drawing a tree-like diagram would be one of the clearest ways to solve this one.
"four nickels, three dimes, and two quarters make a 65-cent",
Do this. For an included count of zero, draw a branch for one coin at a time representing how many coins is available. Four nickels mean, draw a line from "nickels", one line for each count 0, 1, 2, 3, 4. Next coin is dimes and since there are three of them available, draw from each count of the nickel, lines from the nickel for 0, 1, 2, 3 dimes; continue this process. At the finish of drawing these branches for the quarters, find the money sum for each combination drawn. Some of those will equal 65 cents, and some will not.
Another viewpoint, running inline with what I tried to describe, this problem gives 5 ways to use nickes, 4 ways to use dimes, 3 ways to use quarters. That will lead to 5*4*3=60 different combinations of these coins, some of which but not all, will be 65 cents.
Answer by Edwin McCravy(20060)  (Show Source):
You can put this solution on YOUR website!
Besides his quarters he has but 50 cents, so he has
to use at least one quarter.
If he uses 1 quarter, he has 40 cent left to make.
He can do that in two ways, by using 2 dimes and
all four nickels, or all 3 dimes snd 2 nickels.
That's 2 ways.
If he uses both quarters, he has 15 cent left to make.
He can do that in two ways by using 1 dime and 1 nickel,
or no dimes and 3 nickels.
That's 2 more ways.
So there are four ways to make 65 cents.
Edwin
|
|
|
