**Equations**with corrected 4th grade math exercises are advantageous. Thus, the student will have to know the properties for solving equations and the different steps of solving a problem (choice of the unknown, translation of the statement, putting it into an equation, solving it and verifying it, then the conclusion). Understanding this chapter is very important for an eighth grader.

## Series of exercises on equations

### Exercise #1:

Solve the following equations:

### Exercise #2:

I think of a number a, take its triple, subtract 30 and find 3.

What is this number?

### Exercise #3:

I think of a number, add 20 to it, then double the result.

Curiously I find 10 times the number of departure! What is the number you thought of at the beginning?

### Exercise #4:

A 26 year old woman gives birth to triplets. In how many years will the age of the lady be equal to the sum of the ages of the triplets?

*To solve this problem, follow these steps: *

*1) choice of the unknown ; *

*2) equating; *

*3) solving the equation ; *

*4) verification; *

*5) conclusion. *

### Exercise 5:

A father is 42 and his daughter is 12.

We want to find the answer to this question: “In how many years will the father’s age be triple that of his daughter?

To do this, follow the steps below:

1) Choice of the unknown:

x is the number of years sought.

2) Mathematical translation:

Write, as a function of x , the age of the father in years.

Write, as a function of x , the age of her daughter in years.

Translate by an equation: “In x years, the father’s age will be triple the age of his daughter”.

3) Solve the equation.

Then give the answer to the problem posed.

### Exercise #6:

The perimeter of a rectangle is 62 m. We call x its length.

1) Write its width as a function of x and then express its area as a function of x.

We increase its length by 2 m and decrease its width by 1 m.

2) Then express its area as a function of x.

3) Knowing that the area has not changed, calculate x.

### Exercise #7:

A herd is composed of camels and dromedaries. There are 180 heads and 304 bumps. How many animals of each species are there?

### Exercise 8:

A rectangle is twice as long as it is wide. Its perimeter is 66 cm. What are its dimensions?

### Exercise 9:

In the library, there are 8696 books and 104 comics. Each month, the librarian buys 17 books and 3 comics.

In how many months will we exceed 10,000 titles available in this CDI?

### Exercise 10:

Pierre is the eldest. His brother Paul was born two years after him, and their sister Margot was born two years after Paul. Between the three of them, they are 36 years old.

How old is Paul?

### Exercise 11:

At the market this morning, pears were twice as expensive as bananas. I still bought two kilos of pears and six kilos of bananas for 25,20 €.

What was the price of bananas per kilo?

### Exercise 12:

In the comics department, a Gaston Lagaffe costs one euro more than an Asterix, and a Blake and Mortimer costs three euros more than an Asterix.

- Antoine buys three Gaston Lagaffe and two Asterix. Benedicte buys four Asterix and one Blake and Mortimer. Who paid the most?

2. Christophe buys two Gaston Lagaffe and two Blake and Mortimer. For the same price, Diane buys five Asterix. How much does an Asterix cost?

### Exercise 13:

Riri, Fifi and Loulou go together to the charity party and realize that they have between them the glorious sum of 35 €. Riri spends 3 € at the rodeo while Loulou spends 5 € at the shooting range and Fifi watches them play without spending anything. Then they meet again and discover that they each have exactly the same amount of money left as the other two.

How much money did Fifi have to begin with?

### Exercise 14:

A rectangular tennis court of 15 meters by 30 meters is surrounded by a driveway of constant width. The outer perimeter of this driveway is double the size of the tennis court.

How wide is this driveway?

### Exercise 15:

The unknown number: I was added 3 and immediately cut into 4. Then, when that didn’t seem to be enough, they took away the only one I had left! Who was I?

### Exercise 16:

In the yard, there are rabbits and chickens. I counted 16 heads and 44 legs and I am looking for how many rabbits there are.

1. Determine the equation to solve.

2. Test this equation with 5 and then 6 rabbits.

### Exercise 17:

Eight friends attend a concert. Some of them benefit from the reduced rate at 9 € while the others pay the normal rate at 14 €. The group pays a total of 97 €. We are looking at how many of them paid the normal rate.

1. Determine the equation to solve.

2. Test this equation with 5 and then 6 people.

### Exercise 18:

Claire is 12 years old and three times older than her little sister. She wonders in how many years she will be twice as old.

1) Determine the equation to solve.

2) Test this equation with 3 then 4 years.

Skills to be assimilated on first degree equations with one unknown :

- Know the definition of a first degree equation with one unknown and the properties of its solution;
- Solve equations and problems;
- Give the solution set.

These exercises are in accordance with the officialnational education programs.

In addition, you can consult the course on equations in the fourth grade.

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