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Chapter 3: Problem 37

Solve the percent equation. 576 is what percent of 800 ?

Short Answer

Expert verified
576 is 72% of 800.

Step by step solution

01

Identify the Knowns

In the statement '576 is what percent of 800?', the known quantities are 576 and 800. The percentage that 576 is of 800 is what is sought.
02

Write the Equation

In percentage problems, the equation is usually written in the form \(\frac{part}{whole} = \frac{percent}{100}\). In this case, 576 is the part and 800 is the whole. To find the percent, the equation becomes \(\frac{576}{800} = \frac{percent}{100}\).
03

Solve for Percent

To solve for the percentage, cross multiply and solve the resulting equation. In this case, \(576 * 100 = 800 * percent\). Solving for percent gives \(percent = \frac{576 * 100}{800} = 72\).

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Key Concepts

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

Solving Percent Problems
Percent problems involve finding the relationship between a part and a whole. When we say "576 is what percent of 800," we are looking to express 576 as a portion of 800 in percentage terms. To solve these types of problems:
  • Identify the part and the whole. Here, 576 is the part, and 800 is the whole.
  • Use the percent equation, which is given by \( \frac{\text{part}}{\text{whole}} = \frac{\text{percent}}{100} \).
The part is considered as the value or quantity you want to express as a percentage of the whole. By setting up this equation, you can then find the percent by performing calculations.
Cross Multiplication
Cross multiplication is a method used to simplify the solution of equations that involve two ratios. When given an equation like \( \frac{a}{b} = \frac{c}{d} \), you can solve it using cross multiplication.
  • Multiply the numerator of the first fraction by the denominator of the second fraction (\(a \times d\)).
  • Set it equal to the product of the denominator of the first fraction and the numerator of the second fraction (\(b \times c\)).
For our example, the equation \( \frac{576}{800} = \frac{\text{percent}}{100} \) is solved by cross multiplying to get \( 576 \times 100 = 800 \times \text{percent} \). This is an extremely useful technique for solving equations quickly and accurately.
Algebraic Equations
An algebraic equation is an expression that involves variables and constants. In percent problems, the equation \( \frac{576}{800} = \frac{\text{percent}}{100} \) involves solving for the unknown variable 'percent.'
  • The known values are substituted into the simplified equation.
  • Use algebraic manipulation to isolate the variable.
After cross-multiplying in our example, you rearrange the equation as \( \text{percent} = \frac{576 \times 100}{800} \). By calculating on the right side of the equation, you arrive at \(\text{percent} = 72\). This showcases how algebra helps to decode the relationships set within the problem.

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