Problem 23 - Algebra 1

Question

Solve the percent problem. 33 grams is \(22 \%\) of what weight?

Step-by-Step Solution

Answer

The weight that 33 grams is 22% of is approximately 150 grams.

Step 1: Convert the percentage to decimal

The percentage given is 22%. This needs to be converted to decimal form. To convert a percentage to a decimal, one needs to divide it by 100. Hence, 22% becomes \(0.22\) when expressed as a decimal.

Step 2: Formulate the equation

The problem can be represented using the equation: \(total = \frac{part}{\% \, in \, decimal}\). Here, 'part' is the weight that we know (33 grams) and '% in decimal' is the converted decimal of the percentage (0.22). Substitute these values into the equation to obtain \(total = \frac{33}{0.22}\).

Step 3: Solve the equation

Now, it is simple mathematics. Just calculate the divisor of 33 and 0.22 to find the 'total'. When 33 is divided by 0.22, the result is approximately 150.

Key Concepts

Converting Percentages to Decimals

To convert a percentage into a decimal, you basically want to "undo" the percentage format. Percent means per hundred, so any percentage should be divided by 100 to turn it into a decimal. For example, the problem provides us with a percentage of 22%. To change this into a decimal, consider the following simple steps:

• Take the number 22.
• Divide it by 100.

This calculation, 22 divided by 100, results in the decimal 0.22.
It's always the same for any percentage: just shift the decimal point two places to the left. So, 50% becomes 0.50, 5% becomes 0.05, and 22% becomes 0.22.

Equation Formulation

Once the percentage is converted into a decimal, it's time to set up an equation to solve the problem. An equation is a mathematical statement that shows the equality of two expressions. In percentage problems, they often relate the total quantity to a known part.
For this problem, we know:

• The known part, which is 33 grams.
• The percentage in decimal form, which is 0.22.

We need to find the total weight, which is unknown. The relationship between these quantities can be expressed in the equation:\[\text{Total} = \frac{\text{Part}}{\text{Percent in Decimal}}\]Substitute the known values 33 for the part and 0.22 for the percent in decimal, leading to the equation:\[\text{Total} = \frac{33}{0.22}\]This equation gives us a clear path to find the unknown total weight.

Solving Equations

Solving equations can sound intimidating, but it's all about finding the value of an unknown that makes the equation true. With our equation:\[\text{Total} = \frac{33}{0.22}\]We need to perform the division of 33 by 0.22. It's a simple operation when you break it down:

• Divide the number 33 by the decimal 0.22.
• This calculation is done just like any regular division.

Carrying out the division gives approximately 150. Thus, the total weight that 33 grams corresponds to 22% of is 150 grams. Solving equations often requires basic arithmetic operations.
In many cases, like this one, it's merely a matter of organizing data into an equation and calculating.