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Chapter 7: Problem 39

Solve the percent problems with an unknown base. \(30 \%\) of what weight is 69 lb?

Short Answer

Expert verified
230 lb

Step by step solution

01

Understand the problem

We need to find the unknown base weight when we know that 30% of it equals 69 lb. This can be represented by the equation: \( 0.30 \times \text{weight} = 69 \)
02

Set up the equation

To find the unknown weight, set up the equation based on the information given: \( 0.30 \times \text{weight} = 69 \)
03

Solve for the unknown weight

Solve the equation for the unknown weight by dividing both sides by 0.30: \( \text{weight} = \frac{69}{0.30} \)Finally, calculate the result: \( \text{weight} = 230 \)

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Understanding the Unknown Base
When solving percent problems, you sometimes come across an 'unknown base'. This means you have a percentage of a value, but you don't know what the original value (base) is.
For example, in the exercise: '30% of what weight is 69 lb?', we know 30% of a certain weight is 69 lb. But, the actual weight (the unknown base) is what we鈥檙e trying to find.
To solve for the unknown base, you need to set up an equation based on the percentage and the known value.
Setting Up the Percentage Equation
The next step is to set up a 'percentage equation'. This equation ties together the percentage, the unknown base, and the known value.
For our problem: '30% of what weight is 69 lb?'. We start by converting the percentage to a decimal. So, 30% becomes 0.30.
The percentage equation will look like this: \(0.30 \times \text{weight} = 69\).

Here,
  • 0.30: the decimal form of 30%
  • weight: the unknown base we need to find
  • 69: the known value that is 30% of the unknown base
Solving the Equation
Finally, we need to 'solve the equation' to find the unknown base. Start with the percentage equation we already have: \(0.30 \times \text{weight} = 69\).
To isolate the 'weight' (our unknown base), we need to divide both sides of the equation by 0.30.
This gives us:
\(\text{weight} = \frac{69}{0.30}\).
Calculate the result to find the weight:
\(\frac{69}{0.30} = 230\).
So, 30% of 230 lb is 69 lb. Therefore, the unknown base weight is 230 lb.
This shows the step-by-step process of setting up and solving percent problems with an unknown base.

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