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Chapter 6: Problem 9

Translate to an equation and solve. \(150 \%\) of 30 is what?

Short Answer

Expert verified
45

Step by step solution

01

Understand the problem

The problem is asking for the value that represents 150% of 30. This means finding what number 150% of 30 is equivalent to.
02

Convert percentage to decimal

Convert 150% to a decimal by dividing by 100. Thus, 150% becomes \( \frac{150}{100} = 1.5 \).
03

Set up the equation

To find 150% of 30, multiply 30 by the decimal form of 150%. This gives the equation: \( 1.5 \times 30 \).
04

Solve the equation

Multiply 30 by 1.5: \( 1.5 \times 30 = 45 \).
05

Write the solution

The answer to the problem is 45. Therefore, 150% of 30 is 45.

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Key Concepts

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

converting percentages to decimals
Understanding how to convert percentages to decimals is crucial for solving many mathematical problems. A percentage represents a part out of 100. Hence, converting a percentage to a decimal involves dividing by 100. For instance, to convert 150% to a decimal, follow these steps:
  • Take the percentage value: 150.
  • Divide by 100: \(\frac{150}{100} = 1.5\).
So, 150% becomes 1.5 as a decimal. This method applies to any percentage. Converting percentages to decimals simplifies calculations, making it easier to multiply or solve equations. Always remember to divide by 100 when converting.
multiplication
Multiplication is a fundamental mathematical operation. It involves finding the product of two numbers. For example, in the problem, you need to find 150% of 30. After converting 150% to the decimal 1.5, you multiply it with 30. Here's the multiplication step-by-step:
  • Write down the equation: \(1.5 \times 30\).
  • Break it down: Start by multiplying 1.5 by 10 to get 15.
  • Multiply 15 by 3, as 30 is 3 times 10: \(15 \times 3 = 45\).
So, \(1.5 \times 30\) equals 45. By understanding multiplication, you can determine the product of numbers effortlessly, which is essential for solving larger equations as well.
solving equations
Solving equations is about finding the unknown value that makes the equation true. In our exercise, you want to find 150% of 30. Here's how it breaks down:
  • First, you convert 150% to a decimal (1.5).
  • Next, set up the equation: \(1.5 \times 30 = ?\).
  • Perform the multiplication: \(1.5 \times 30 = 45\).
The solution is 45. By solving this equation, you've determined that 150% of 30 is 45. This technique can be applied to similar problems. Focus on converting percentages first, setting up the equation correctly, and solving step-by-step. This approach simplifies complex problems and ensures accuracy in your answers.

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Most popular questions from this chapter

A coupon allows a couple to have \(\$ 10\) subtracted from their dinner bill. Before subtracting \(\$ 10\), however, the restaurant adds a tip of \(20 \%\). If the couple is presented with a bill for \(\$ 40.40\), how much would the dinner (without tip) have cost without the coupon?

In Kansas, 47,000,000 acres are farmland. About \(5 \%\) of all the farm acreage in the United States is in Kansas. What is the total number of acres of farmland in the United States?

Solve. $$ \frac{x}{12}=\frac{24}{16} $$

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