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