Respuesta :
Answer:
15 years , 12 years , 8 years.
Step-by-step explanation:
Given:
John is 3 years older than Jim.
Jim is 4 years less than twice David’s age.
Ages of three boys add up to 35.
Question asked:
How old are the three boys?
Solution:
Let age of David = [tex]y[/tex]
Let age of Jim = [tex]x[/tex]
Then age of John will be = [tex]x + 3[/tex]
As Jim is 4 years less than twice David’s age
Equation will be , [tex]x = 2y - 4[/tex]
Multiplying both side by 2
= [tex]2x = 4y - 8[/tex] (let equation 1 )
As ages of three boys add up to 35.
Equation will be,[tex]x + (x + 3) + y = 35[/tex]
= [tex]2x + 3 + y = 35[/tex]
Subtracting both side by 3
= [tex]2x + y = 32[/tex]
= [tex]2x = - y + 32[/tex] (let equation 2 )
subtracting equation 1 and 2,we get
= [tex]2x = - y + 32[/tex]
= [tex]2x = 4y - 8[/tex]
= [tex]0 = - 5y + 40[/tex]
= [tex]5y = 40[/tex]
dividing both side by 5
[tex]= y = 8[/tex] (David ages)
Then ( age of Jim) [tex]x = 2y - 4[/tex]
[tex]x = 2 \times8 - 4[/tex]
= [tex]16 - 4[/tex]
= [tex]12 years[/tex]
Then age of John will be, [tex]x + 3[/tex]
[tex]= 12 + 3[/tex]
= [tex]15 years[/tex]
Thus, age of John = 15 years
Age of Jim = 12 years
Age of David = 8 years
The required age of David is y = 8 , Jim is x = 12 and the John is x+3 = 12+ 3 = 15 .
Let age of David = y
Age of Jim = x
The age of John will be = x+3
We have to find ;
How old are the three boys.
According to the question,
As Jim is 4 years less than twice David’s age,
The required equation is ,
x = 2y - 4
As ages of three boys add up to 35.
Equation is,
x + (x + 3 ) +y = 35
2x + y = 35 - 3
2x + y = 32
Solving the equations ,
put the value of equation in the equation 2
2 ( 2y -4 ) +y = 32
4y - 8 + y = 32
5y = 32 + 8
5y = 40
y = [tex]\frac{40}{5}[/tex]
y = 8
The age of David is y = 8 .
Put the value of y in the equation 1
x = 2 (8) - 4
x = 16 - 4
x = 12
The age of jim is x = 12
And the age of john is = x+ 3 = 12 +3 = 15 .
Adding the age of three boys = 15 + 12 + 8= 35
Hence, The required age of David is y = 8 , Jim is x = 12 and the John is x+3 = 12+ 3 = 15 .
For the more information about System of equations click the link given below.
https://brainly.com/question/12895249
