bert is twice as old as jeff. John is 4 years younger than bert. The sum of their ages is 31. How old is bert?
x = Bert's age
y = Jeff's age
z = John's age
Bert is twice as old as jeff mean:
x = 2 y
This is the same:
y = x / 2
John is 4 years younger than Bert mean:
z = x - 4
The sum of their ages is 31 mean:
x + y + z = 31
Now:
x + y + z = 31
x + x / 2 + x - 4 = 31
2 x / 2 + x / 2 + 2 x / 2 - 4 = 31
5 x / 2 - 4 = 31
Add 4 to both sides
5 x / 2 - 4 + 4 = 31 + 4
5 x / 2 = 35
Mutiply both sides by 2
5 x = 2 ∙ 35
5 x = 70
Divide both sides by 5
x = 70 / 5
x = 14
y = x / 2
y = 14 / 2
y = 7
z = x - 4
z = 14 - 4
z = 10
x = Bert's age = 14
y = Jeff's age = 7
z = John's age = 10
Bert is 14 yrs old.
Jeff's age ---- x
Bert's age --- 2x
John's age --- 2x - 4
x + 2x + 2x-4 = 31
5x = 35
x = 7
so Bert is 14
To solve this problem, we can set up equations based on the given information. Let's assign variables to represent the ages of each person.
Let's say Bert's age is represented by "B," Jeff's age is represented by "J," and John's age is represented by "N."
Given that Bert is twice as old as Jeff, we can write the equation:
B = 2J
We also know that John is 4 years younger than Bert, so we can write the equation:
N = B - 4
Finally, we are given that the sum of their ages is 31, so we can write the equation:
B + J + N = 31
Now we can use these equations to find the values of the variables.
Substituting B = 2J into the third equation, we get:
2J + J + N = 31
Combining like terms, we have:
3J + N = 31
Substituting N = B - 4 into the above equation, we get:
3J + B - 4 = 31
Rearranging the equation, we have:
B + 3J = 35
From the first equation, B = 2J, we can substitute B into the equation above:
2J + 3J = 35
Simplifying, we have:
5J = 35
Dividing both sides by 5, we get:
J = 7
Now, substituting J = 7 into the first equation, we find:
B = 2(7) = 14
Therefore, Bert is 14 years old.