Example 1
Double a number subtracted from 20 equals 100. What's the number?
A number: x
Double the number: 2x
As we are subtracting 2x from 20 the equation will be:
20 - 2x = 100
solving the equation
20 - 2x = 100
– 2x – 20 + 20 = 100 – 20 (we add 20 to both sides of the equation)
– 2x = 80 (– 1)
2x = – 80
x = - 80
2
x = – 40
So the number is equal to – 40.
Example 2
Triple a number added to its double makes 600. What's the number?
A number: x
Triple this number: 3x
Double this number: 2x
Triple a number added to its double gives 600: 3x + 2x = 600
Solving the equation:
3x + 2x = 600
5x = 600
x = 600/5
x = 120
We have the number equal to 120.
Example 3
What number am I? Double my predecessor, minus 3, equals 25.
A number: x
Predecessor: x – 1
Double my predecessor minus 3: 2(x – 1) – 3 = 25
solving the equation
2(x – 1) – 3 = 25 (apply distribution method)
2x – 2 – 3 = 25
2x – 5 = 25
2x = 25 + 5
2x = 30
x = 30/2
x = 15
The number is equal to 15.
Example 4
Carlos had a certain amount of money, he went to the mall and spent 1/3 of the amount on the purchase of a magazine, he spent 1/4 of the amount on the purchase of a CD and still had R$25.00. How much money did Carlos have?
Amount: x
One third of the amount: 1/3x
A quarter of the amount: 1/4x
Problem equation: (1/3)x + (1/4)x + 25 = x
MMC (3.4) = 12
(4/12)x + (3/12)x + 300 = (12/12)x (simplifying the denominators)
4x + 3x + 300 = 12x
12x - 4x - 3x = 300
12x - 7x = 300
5x = 300
x = 300/5
x = 60
Carlos had the amount of R$ 60.00.
Example 5
The 44 7th grade A students at a school represent 40% of all 7th grade students at that same institution. How many 7th graders are there at this school?
Students: x
40% = 40/100 = 2/5 of students
2/5 of x
(2/5)x = 44
2x = 44 * 5
2x = 220
x = 220/2
x = 110
Result: The school has 110 students in the 7th grade.
by Mark Noah
Graduated in Mathematics
Brazil School Team
Equation - Math - Brazil School
Source: Brazil School - https://brasilescola.uol.com.br/matematica/problemas-envolvendo-uso-equacoes.htm