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Chapter 6: Problem 306

In the following exercises, translate to a proportion. 90 is 150\(\%\) of what number?

Short Answer

Expert verified
x = 60

Step by step solution

01

- Understand the Problem

We need to find the number 'x' such that 90 is 150% of 'x'. This can be translated into an equation.
02

- Set up the Equation

Since 150% can be written as 1.5 in decimal form, we can set up the equation as follows: 90 = 1.5x
03

- Solve for x

To find 'x', divide both sides of the equation by 1.5: \( x = \frac{90}{1.5} \)
04

- Calculate the Answer

Perform the division to find the value of 'x': \( x = \frac{90}{1.5} = 60 \)

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Key Concepts

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

Percentages
Percentages are a way to express a number as a fraction of 100. They are useful for comparing proportions and quantifying changes. In calculations, percentages such as 150% can be converted to their decimal equivalent by dividing by 100. For example, 150% becomes 1.5. This conversion is essential when dealing with algebraic equations involving percentages.

In the given exercise, we need to find an unknown number 'x' such that 90 is 150% of it. Here, 150% is converted to 1.5 to simplify the equation setup.
Algebraic Equations
An algebraic equation is a mathematical statement that shows the equality of two expressions. To solve algebraic equations, we use various operations to isolate the unknown variable on one side of the equation.

In this exercise, we set up the equation by translating the given percentage statement into an algebraic form: 90 = 1.5x. This means 90 is equal to 1.5 times some number 'x'.
To solve for 'x', we need to isolate it. We do this by performing the inverse operation鈥攄ivision鈥攊n the next step.
Division
Division is one of the fundamental arithmetic operations. It involves splitting a number into equal parts. When dealing with algebraic equations, we often use division to solve for an unknown variable.

In our exercise, after setting up the equation 90 = 1.5x, we solve for 'x' by dividing both sides by 1.5. This ensures that we isolate 'x' on one side of the equation:
\[ x = \frac{90}{1.5} \]
Performing the division, we find that 'x' equals 60. Thus, 90 is 150% of 60.

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Most popular questions from this chapter

In the following exercises, solve the percent problem. Kyle bought a bicycle in Denver where the sales tax was 7.72\(\%\) of the purchase price. The purchase price of the bicycle was \(\$ 600\) . What was the total cost?

Solve the applications of percents. One serving of trail mix has 67 grams of carbohydrates, which is 22% of the recommended daily amount. What is the total recommended daily amount of carbohydrates?

Dimple gets paid \(\$ 3,200\) per month. She pays \(\$ 960\) a month for rent. What percent of her monthly pay goes to rent?

Tipping At the campus coffee cart, a medium coffee costs \(\$ 1.65\) . Mary Anne brings \(\$ 2.00\) with her when she buys a cup of coffee and leaves the change as a tip. What percent tip does she leave?

In the following exercises, translate and solve using proportions. 6\(\%\) of what number is \(\$ 24 ?\)
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