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Chapter 6: Problem 28

Translate to a proportion. Do not solve. $$ 63.7 \text { is } 65 \% \text { of what? } $$

Short Answer

Expert verified
0.65x = 63.7

Step by step solution

01

Identify the Parts of the Problem

Identify the given values and the unknown. The given values are 63.7 (part) and 65% (percentage). The unknown is the whole.
02

Convert Percentage to Decimal

Convert the percentage to a decimal by dividing by 100. So, 65% becomes 0.65.
03

Set Up the Proportion Equation

Use the relationship of part, whole, and percentage. The formula is \( \text{percentage} \times \text{whole} = \text{part} \). Substitute the known values: \( 0.65 \times \text{whole} = 63.7 \).
04

Write the Proportion

Rewrite the equation to explicitly show it as a proportion: \[ 0.65x = 63.7 \]. The proportion is set up.

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Key Concepts

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

Percentage Conversion
Percentages are a way to express numbers as parts of 100. To convert a percentage to a decimal, you simply divide the percentage by 100. For example, if you have 65%, you convert it to a decimal like this: \( \frac{65}{100} = 0.65 \). Converting percentages to decimals is crucial because it makes mathematical calculations easier, especially when you're setting up equations.
Finding the Whole
When given a percentage and a part of the whole, you can find the whole using a proportion. In the problem statement, 63.7 is 65% of some unknown whole. Here鈥檚 how to approach this:
First, understand that the part (63.7) and the percentage (65%) are related by the whole. We convert the percentage to a decimal (0.65 in this case) and use the equation: \( \text{percentage} \times \text{whole} = \text{part} \). Plug in the known values: \( 0.65 \times \text{whole} = 63.7 \). This equation can then be solved to find the whole.
Mathematical Equations
Mathematical equations are statements that show the equality of two expressions. In this problem, we use the equation \( 0.65x = 63.7 \), where \(x\) represents the whole we need to find. This proportion equation stems from the general formula for percentages: \( \text{percentage} \times \text{whole} = \text{part} \). The variable \(x\) stands in for the unknown value we seek. By setting up the equation as a proportion, we can solve for \(x\) to determine the whole. Solving such equations involves isolating the variable, often through division in this context.

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Most popular questions from this chapter

Given normal use, an Americanmade car will depreciate \(25 \%\) of its original cost in the first year and \(14 \%\) of its remaining value in the second year. What is the value of a car at the end of the second year if its original cost was $$\$ 36,400 ?$$ $$\$ 28,400 ?$$ $$\$ 26,800 ?$$

Solve. Mia's Boutique borrows \(\$ 10,000\) at \(9 \%\) for 60 days. Find (a) the amount of interest due and (b) the total amount that must be paid after 60 days.

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A monthly mortgage payment increases from $$\$ 840$$ to $$\$ 882 .$$ What is the percent increase?
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