Question

stuart bought a candy bar that cost 90 cents. he gave the cashier a $1 bill. which of the following tree diagrams shows all of the ways the cashier can give correct change using pennies, nickels, and dimes?

Explanation:

Step1: Calculate the change amount

Stuart gave a $\$1$ bill ($100$ cents) for a $90$-cent candy bar. The change is $100 - 90=10$ cents.

Step2: Check each tree - diagram branch

• A dime is $10$ cents. A nickel is $5$ cents. A penny is $1$ cent.
• For the first branch (left - most): $1$ dime ($10$ cents) is valid.
• Second branch: $0$ dimes, $1$ nickel ($5$ cents), $5$ pennies ($5$ cents). $5 + 5=10$ cents (valid).
• Third branch: $0$ dimes, $2$ nickels ($2\times5 = 10$ cents) (valid).
• Fourth branch: $0$ dimes, $0$ nickels, $10$ pennies ($10$ cents) (valid).

Answer:

The left - most tree - diagram (the one with \(1\) dime at the top) is correct. Because when calculating the change of \(10\) cents (\(100 - 90\)), having \(1\) dime (\(10\) cents) is a valid way to make the change. The other branches also make \(10\) cents (\(0\) dimes \(+1\) nickel \(+5\) pennies \(=10\) cents, \(0\) dimes \(+2\) nickels \(=10\) cents, \(0\) dimes \(+0\) nickels \(+10\) pennies \(=10\) cents), but the question is about the tree - diagram that shows all ways. The left - most branch is the first and a valid way to start representing the change (as a single dime is a simple and correct way to make \(10\) cents change).