# How to solve interest problems • How to solve problems with interest
• How to calculate the proportion
• How to learn to count percentages
• 1) Paper 2) Pen 3) Calculator

According to the vocabulary of Ozhegov Sergey Ivanovich, the percent is called the hundredth share (part) of the whole and is indicated by the sign%. The hundredth fraction can be written like this:

In the role of the whole, i.e. 100%, anything can appear: any number, a bunch of grapes, a keg of honey or a pension.

1) Find 18% of the pension equal to 6,122 p.

6 122 p. * 18% = 6 122 p. * 18/100 = 6 122 p. * 0.18 = 1101.96 p.

2) Pour a barrel of honey into 8 cans. Give 3 cans to guests. How many percent of the honey from the barrel did you give away? How much do you have left?

3/8 or 0,375 of the barrel you have given away. Convert to percent, multiplying by 100. You gave 37.5% of the honey that you had. It remains 5/8 = 0.625 * 100% = 62.5%.

All interest tasks are easy to solve with proportion.

Find 82% of the number 506.

X is 82%, where X is the unknown to be found.

506 / X = 100% / 82%, or immediately 506 * 82% = X * 100%

X = 506 * 82% / 100% = 414.92

Percentage (%) as a unit of measurement declined.

First type
Find the percentage of the given number.

The average salary in your organization is 20 thousand rubles. Next year they promise to increase it by 20%. How much will the expected salary increase next year?

X = 20 thousand p. * 20% / 100% = 4 thousand p.

The expected average salary will increase by 4 thousand rubles. and amount to 24 thousand p.

Find the number by percentage.

40% of the tomato in the box, which amounted to 5 kg, turned out to be green. How much is a kilogram of tomato in a box?

X = 5kg * 100% / 40% = 12.5 kg

Find the percentage of one number through another.

In the morning, Peter usually drinks 1 cup of tea, and in the evening - 4. How many percent of the evening volume of tea cups does he drink in the morning?

X = 1 cup * 100% / 4 cups = 25%

### Interest in math.

What interest in math? How to decide interest tasks? These questions come up, alas, all of a sudden ... When a graduate reads the exam task. And they confuse him. But in vain. These are very simple concepts.

The only thing you need to remember is iron - what is one percent. This concept is master key to solving problems on interest, and to work with interest in general.

One percent is one hundredth of a number. And that’s it. No more wisdom.

A reasonable question - and the hundredth part what date? But that number, which is discussed in the task. If it talks about price, one percent is one hundredth of the price. If it’s about speed, one percent is one hundredth of a speed. And so on. It is clear that the number in question is always 100%. And if there is no number itself, then percentages do not make sense ...

Another thing is that in complex problems the number itself will be so hidden that you won’t find it. But we are not yet swinging at the difficult. Deal with percent in math.

I accent words for nothing one percent, one hundredth. Remembering what one percent, you can easily find two percent, and thirty four, and seventeen, and one hundred twenty six! You will find as much as you need.

And this, by the way, is the main skill for solving problems at interest.

Let's find 3% of 400. First we find one percent. It will be one hundredth, i.e. 400/100 = 4. One percent is 4. But how many percent do we need? Three. So we multiply 4 by three. Get 12. That's it. Three percent of 400 is 12.

5% of 20 it will be 20 divided by 100 (one hundredth - 1%), and multiplied by five (5%):

5% of 20 it will be 1. That's it.

Nowhere is easier. Let's fast, before we forget, let's practice!

Find how much will be:
5% of 200 rubles.
8% of 350 kilometers.
120% of 10 liters.
15% of 60 degrees.
4% of excellent students from 25 students.
10% of doubles from 20 people.

Answers (in complete disarray): 9, 10, 2, 1, 28, 12.

These numbers are the number of rubles, degrees, students, etc. I did not write how much something to solve was more interesting ...

And if we need to write x% from some number, for example, from 50? Yes, all the same. One percent of 50 is how much? Right, 50/100 = 0.5. And we have these percentages - x. Well, multiply 0.5 by x! We get that x% from 50 it is - 0.5x.

I hope that such interest in math you got it. And you can easily find any number of percent of any number. It's simple. You now can afford about 60% of all tasks for interest! Already more than half. Well, are we getting the rest? Well, as you say!

In percent tasks, the opposite is often encountered. They give us values (whatever), but you need to find interest. We will master this simple process.

3 people out of 120 - how many percent? Do not know? Well then, let it be x percent.

We calculate x% from 120 people. In humans. This we can do. 120 divide by 100 (calculate 1%) and multiply by x (calculate x%) We get 1.2x.

xpercent from 120 people, this is 1.2xperson. And we have three such people. It remains to equate:

We recall that for X we took the amount of interest. So 3 people from 120 people - this is 2.5%.

It is possible in another way. Do with a simple savvy, without any equations. Considerhow many times3 people less than 120? Divide 120 by 3 and get 40. Therefore, 3 is less than 120 by 40 times.

The desired number of people as a percentage will be as many times less than 100%. After all, 120 people - this is 100%. Divide 100 by 40, 100/40 = 2.5

There is still a way of proportions, but this, in essence, is the same in a shortened version. All of these methods are correct. As you prefer, more familiar, more understandable - consider it.

Calculate how many percent are:
3 people out of 12.
10 rubles from 800.
4 textbooks from 160 books.
24 correct answers to 32 questions.
2 guessed answers to 32 questions.
9 hits from 10 shots.

Answers (in a mess): 75%, 25%, 90%, 1.25%, 2.5%, 6.25%.

In the process of computing, you may well encounter fractions. Including inconvenient, such as 1.3333333 ... And who told you to use the calculator? Yourself? Do not. Count without calculatoras written in the Fraction topic. There are all kinds of percentages ...

So we have mastered the transition from values ​​to percentages and vice versa. You can take on tasks.

## Examples of solving problems on interest

30 corresponds to 100% x corresponds to 15%

 30 = 100% x 15%

solve the resulting equation

 x = 30 · 15% = 4.5 100%
Answer: 15% of 30 is 4.5.

20 corresponds to 100% 35 corresponds to x

 20 = 100% 35 x

solve the resulting equation

 x = 35 · 100% = 175% 20
Answer: 35 is 175% of 20.

x corresponds to 100% 20 corresponds to 5%

 x = 100% 20 5%

solve the resulting equation

 x = 20 · 100% = 400 5%

When studying interest, you will also be useful:

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My name is Dovzhik Mikhail Viktorovich. I am the owner and author of this site, I have written all the theoretical material, and also developed online exercises and calculators that you can use to study mathematics.

# Tip 3: How to solve a task from the exam in algebra • Leaf, pen, ruler.

Consider the task (B1). Example: A ballpoint pen costs 40 rubles. What is the largest number of such pens that can be bought for 300 rubles after increasing the price of pens by 10%? To get started, find out how much the ballpoint pen began to cost after raising the price. To do this, divide 40 by 100, multiply by 10 and add 40. The new price of the pen is 44 rubles. And now divide 300 by 44. Answer: 6.

Task (B2). You can easily solve this task on schedule, just be very careful.

Task (B3). Example: Find the root of equation 7 in degree (y - 2) equals 49. First imagine 49 as 7 in second degree. Now you get the equation: y - 2 = 2. Solving it, you get the answer: 4.