age problem?

Question

lyle is 15 years old now and her mother is 38 years old now. in how many years will lyle be half as old as her mother?

Answer 1

2(15+x) = 38+x
30 + 2x = 38 + x
x = 8 which is the answer
2(15+8) = 2(23) = 46 = 38+8

Answer 2

To help us solve this problem, let's make a table.

Now - - - - - - - - In X years
____ - - - - - - - - ________
15 - - - - - - - - - - - 15 + x
38 - - - - - - - - - - - 38 + x

The first row represents the age of Lyle, and the secod row represents the age of Lyle's mother. The variable x obviously repreesents the number of years.

What we want to know is when Lyle will be half as old as her mother. This is represented by the following equation:

15 + x = (1/2) (38 + x)

As you can see, we made an equation after x years have passed, and "half as old as her mother" is represents as 1/2 as old as her mother in x years, which is how the table helped. So now we solve.

15 + x = (1/2) (38 + x)

Let's get rid of that pesky fraction by multiplying both sides by 2.

2(15 + x) = 38 + x

Expand the left hand side, to get

30 + 2x = 38 + x

And now, move all x terms to the left hand side and everything else to the right hand side.

2x - x = 38 - 30
x = 8

Therefore, in 8 years, Lyle will be half as old as her mother.

Let's check:

In 8 years, Lyle will be 15 + 8 = 23 years old.
In 8 years, Lyle's mother will be 38 + 8 = 46 years old.

23 is half of 46! Yay!

Answer 3

Okay, here we go.
(l is Lyle; m is mother; x is the answer; how many years it will take).

(15+x)=(1/2)(38+x) (Next, we distribute)
15+x=19+(1/2)x (Subtract 15 from both sides)
x=4+(1/2)x (Subtract half x from both sides)
(1/2)x=4 (Multiply half x by two to get the value of x)
x=8 years

Now, if you want to know why we add x to both sides of the equation, remember that if it's in 8 years, both lyle and the mother will be older. If you're wondering why we put 38+x in parentheses, keep in mind we want to know when lyle will be half the mother age in that many years, not her age now.

Answer 4

This can be solved algebraically

In x years, lyle will be 15+x years old while his mother wil be 38+x years old

15+x = (1/2)(38+x)
30+2x = 38+x
x = 8

Therefore, in 8 years, lyle will be half as old as her mother.

Answer 5

Lets say in x years Lyle will be half as old as her mother.

15+x = (1/2)(38+x)

Multiply by 2,

30+2x = 38+x

which leads to x = 8 years.

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Also, you can do mental math.

Since the difference in ages is a constant 38-15 = 23, when Lyle is 23 years old, he will be half as old as her mother. Therefore, in 8 years, Lyle will be 23 years old and thus will be half as old as her mother.

Answer 6

8

Answer 7

- in the present -
Iyle's age= 15
mother's age= 38
-after x years-
Iyle's age = 15+x
mother's age = 38+x
according to the question, at these ages,
Iyle's age = 1/2 of mother's age
therefore,
15+x = 1/2(38+x)
15+x = 38/2 + x/2
15+x = 19 +x/2
x - x/2 = 19-15
2x/2 - x/2 = 4
x/2 = 4
x = 4*2 = 8
therefore, after 8 yrs,
Iyle's age=15+8=23 yrs
mother's age=38+8=46yrs
23=46/2
Iyle's age= 1/2 of mother's age

Answer 8

8 years from now Lyle will be 23 and her mom will be 46.

Answer 9

Not sure why these people aren't smart enough to just look at it an see that it's 8 years. Don't need all the math, people are just trying to get best answer by trying to look smart.