Jane is x years old today. Her brother Kenny is 4 years older. After seven years their total combined age will be 24 years. Write a linear equation for their total combined age after seven years. Fine James age today.

Now:

Jane --- x
Kenny --- x+4

after 7 years:
Jane --- x+7
Kenny -- x+11

at that time:
x+7 + x+11 = 24
2x = 6
x=3

Jane is now 3, (where does James come in ? )

...... If you have to do it using 2 variables ....
jane now --- x
Kenny now -- y

y - x = 4 (#1)

x+7 + y+7 = 24
x+y = 10 (#2)
add #1 and #2
2y = 14
y = 7
x = 3
Same answer, but the first method looked easier.

Let's solve this step-by-step.

Step 1: Let's assume Jane's age today as x.

Step 2: Since her brother Kenny is 4 years older, his age today would be x + 4.

Step 3: After seven years, Jane's age will be x + 7, and Kenny's age will be (x + 4) + 7 = x + 11.

Step 4: Their total combined age after seven years will be (x + 7) + (x + 11).

Step 5: Simplifying the equation, we have:

Total combined age after seven years = (x + 7) + (x + 11)

Total combined age after seven years = 2x + 18

So, the linear equation for their total combined age after seven years is:

Total combined age = 2x + 18

Step 6: To find Jane's age today, we can set her age today (x) equal to her age after seven years (x + 7) minus seven.

Jane's age today = (x + 7) - 7

Jane's age today = x

Therefore, Jane is x years old today.

Thus, we cannot determine Jane's age today without additional information.

To solve this problem, let's first define some variables:

Let's say Jane's age today is x.
Then Kenny's age today would be (x + 4) since he is 4 years older.

After seven years, Jane's age would be (x + 7) and Kenny's age would be ((x + 4) + 7) which simplifies to (x + 11).

Now, the problem states that the total combined age after seven years will be 24 years. We can now write the equation:

(x + 7) + (x + 11) = 24

Simplifying the equation, we combine like terms:

2x + 18 = 24

To isolate the variable on one side, we subtract 18 from both sides of the equation:

2x = 6

Finally, we divide both sides of the equation by 2 to solve for x:

x = 3

Therefore, Jane is 3 years old today.

x and x+4 forever

x + 7 + x+ 4 +7 = 2x + 18 = 24 after seven years
2x = 6
x = 3
x+4 = 7

so James is 3 now