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T-Willy got 128 pounds of honey from his hive. If this was a 60 percent increase from last year, how much honey did he get last year?

Draw a diagram as an aid in solving the problem.

Answer :

To find out how much honey T-Willy got last year, we need to determine the original amount before the 60% increase that resulted in 128 pounds this year. Here’s a step-by-step guide on how to solve this:

1. Understand the Problem Statement:
The problem states that this year T-Willy collected 128 pounds of honey, which is a 60% increase from the amount he collected last year.

2. Set Up the Relationship with Percentages:
If the amount of honey collected last year is represented as 100%, then this year's honey (128 pounds) is 160% of last year's honey. This is because we have the original 100% plus an additional 60%.

3. Create an Equation to Solve for Last Year's Honey:
Let [tex]\( x \)[/tex] represent the amount of honey T-Willy collected last year. Since 128 pounds represents a 160% total of [tex]\( x \)[/tex], we can write the equation:
[tex]\[
1.60 \cdot x = 128
\][/tex]

4. Calculate the Amount of Honey Collected Last Year:
To find [tex]\( x \)[/tex], divide both sides of the equation by 1.60:
[tex]\[
x = \frac{128}{1.60}
\][/tex]

5. Perform the Calculation:
By doing the division, we find:
[tex]\[
x = 80
\][/tex]

So, T-Willy collected 80 pounds of honey last year.

6. Verification (Optional):
To ensure this answer makes sense, you can check by calculating 60% of 80, which is 48. Adding this to 80, you get the 128 pounds collected this year, confirming that our calculation is correct.

Thus, T-Willy got 80 pounds of honey from his hive last year.

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