# Solving Problems With Proportions

This unknown quantity will be represented by x in our proportion. Substitute: Now we can substitute these values into our proportion.becomes Solve: Cross multiply and we get: 20x = 800 Divide both sides by 20 to solve for x and we get: x = 40 Solution: 8 is 40% of 20. Note that in Problem 1 we did not have to cross multiply to solve the proportion.

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Analysis: In this problem, you are being asked 8 is what percent of 20?

You are given two numbers from the proportion above and asked to find the third.

We often get reports about how much something has increased or decreased as a percent of change.

The percent of change tells us how much something has changed in comparison to the original number.

To solve problems with percent we use the percent proportion shown in "Proportions and percent".

$$\frac=\frac$$ $$\frac\cdot =\frac\cdot b$$ $$a=\frac\cdot b$$ x/100 is called the rate.$0-150=90$$Then we find out how many percent this change corresponds to when compared to the original number of students$$a=r\cdot b$$=r\cdot 150$$ $$\frac=r$$$[[

$$\frac=\frac$$ $$\frac\cdot =\frac\cdot b$$ $$a=\frac\cdot b$$ x/100 is called the rate.

$$240-150=90$$ Then we find out how many percent this change corresponds to when compared to the original number of students $$a=r\cdot b$$ $$90=r\cdot 150$$ $$\frac=r$$ $$0.6=r= 60\%$$ We begin by finding the ratio between the old value (the original value) and the new value $$percent\:of\:change=\frac=\frac=1.6$$ As you might remember 100% = 1.

Since we have a percent of change that is bigger than 1 we know that we have an increase.

In this problem, the percent is the unknown quantity! Looking at this problem, it is clear that 8 is the part and 20 is the whole.

We need to figure out how to find this unknown quantity. Similarly, in the statement, "One number is some percent of another number.", the phrase "one number" represents the part and "another number" represents the whole.

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$$\frac=\frac$$ $$\frac\cdot =\frac\cdot b$$ $$a=\frac\cdot b$$ x/100 is called the rate.$$240-150=90$$ Then we find out how many percent this change corresponds to when compared to the original number of students $$a=r\cdot b$$ $$90=r\cdot 150$$ $$\frac=r$$ $$0.6=r= 60\%$$ We begin by finding the ratio between the old value (the original value) and the new value $$percent\:of\:change=\frac=\frac=1.6$$ As you might remember 100% = 1.Since we have a percent of change that is bigger than 1 we know that we have an increase.In this problem, the percent is the unknown quantity! Looking at this problem, it is clear that 8 is the part and 20 is the whole.We need to figure out how to find this unknown quantity. Similarly, in the statement, "One number is some percent of another number.", the phrase "one number" represents the part and "another number" represents the whole.Every statement of percent can be expressed verbally as: "One number is some percent of another number." Percent statements will always involve three numbers. Thus the statement, "One number is some percent of another number.", can be rewritten: "One number is some percent of another number.", becomes, "The part is some percent of the whole." From previous lessons we know that the word "is" means equals and the word "of" means multiply.Thus, we can rewrite the statement above: The statement: "The part is some percent of the whole.", becomes the equation: the part = some percent x the whole Since a percent is a ratio whose second term is 100, we can use this fact to rewrite the equation above as follows: the part = some percent x the whole becomes: the part = x the whole Dividing both sides by "the whole" we get the following proportion: Since percent statements always involve three numbers, given any two of these numbers, we can find the third using the proportion above. Problem 1: If 8 out of 20 students in a class are boys, what percent of the class is made up of boys?The percent is the unknown quantity in this problem. Identify: The phrase 8 is means that 8 is the part.The phrase what percent tells us that percent is the unknown quantity.There are two different methods that we can use to find the percent of change.We begin by subtracting the smaller number (the old value) from the greater number (the new value) to find the amount of change.

]].6=r= 60\%$$We begin by finding the ratio between the old value (the original value) and the new value$$percent\:of\:change=\frac=\frac=1.6 As you might remember 100% = 1.Since we have a percent of change that is bigger than 1 we know that we have an increase.In this problem, the percent is the unknown quantity! Looking at this problem, it is clear that 8 is the part and 20 is the whole.We need to figure out how to find this unknown quantity. Similarly, in the statement, "One number is some percent of another number.", the phrase "one number" represents the part and "another number" represents the whole.Every statement of percent can be expressed verbally as: "One number is some percent of another number." Percent statements will always involve three numbers. Thus the statement, "One number is some percent of another number.", can be rewritten: "One number is some percent of another number.", becomes, "The part is some percent of the whole." From previous lessons we know that the word "is" means equals and the word "of" means multiply.Thus, we can rewrite the statement above: The statement: "The part is some percent of the whole.", becomes the equation: the part = some percent x the whole Since a percent is a ratio whose second term is 100, we can use this fact to rewrite the equation above as follows: the part = some percent x the whole becomes: the part = x the whole Dividing both sides by "the whole" we get the following proportion: Since percent statements always involve three numbers, given any two of these numbers, we can find the third using the proportion above. Problem 1: If 8 out of 20 students in a class are boys, what percent of the class is made up of boys?The percent is the unknown quantity in this problem. Identify: The phrase 8 is means that 8 is the part.The phrase what percent tells us that percent is the unknown quantity.There are two different methods that we can use to find the percent of change.We begin by subtracting the smaller number (the old value) from the greater number (the new value) to find the amount of change.

## Comments Solving Problems With Proportions

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