Jake is 15 years older than liz while naida is 19 years younger than liz. Find their present ages if age in 4 years is 5 more than the sum of naida's age 7 years from now and liz's age 11 years ago
Liz's present age --- x
Jake's present age --- x+15
Naida's present age --- x-19
Guessing that your typo is: Find their present ages if Jake's age in ....
Jake's age 4 years from now: x+15 + 4 = x + 19
naida's age 7 years from now = x-19 + 7 = x - 12
liz's age 11 years ago = x-11
Find their present ages if Jake's age in 4 years is 5 more than the sum of naida's age 7 years from now and liz's age 11 years ago
---> x+19 = (x-12) + (x-11) + 5
x+19 = 2x - 18
x = 37
State their present ages by going back to my definitions
Verify my answer after checking my arithmetic
Let's represent the present age of Liz as "x".
According to the given information, Jake is 15 years older than Liz, so Jake's age is "x + 15" years.
Naida is 19 years younger than Liz, so Naida's age is "x - 19" years.
In 4 years, the sum of Naida's age 7 years from now (x - 19 + 7) and Liz's age 11 years ago (x - 11) is 5 more than the result of the addition.
Therefore, the equation becomes:
(x - 19 + 7) + (x - 11) + 5 = x + 15
Let's solve this equation step-by-step:
First, simplify the equation:
(x - 12) + (x - 11) + 5 = x + 15
Next, combine like terms:
2x - 23 + 5 = x + 15
Simplifying further:
2x - 18 = x + 15
Subtract x from both sides to isolate the variable:
2x - x - 18 = x -x + 15
Simplifying again:
x - 18 = 15
Finally, add 18 to both sides to solve for x:
x - 18 + 18 = 15 + 18
Simplifying further:
x = 33
Therefore, Liz's present age is 33 years.
Now we can find the ages of Jake and Naida by substituting the value of x into their respective expressions:
Jake's age = x + 15 = 33 + 15 = 48 years
Naida's age = x - 19 = 33 - 19 = 14 years
So, Jake's present age is 48 years, and Naida's present age is 14 years.
To find their present ages, let's assign variables to represent each person's age:
Let's call Jake's age J.
Let's call Liz's age L.
Let's call Naida's age N.
According to the given information, we know that Jake is 15 years older than Liz, so J = L + 15.
Additionally, we know that Naida is 19 years younger than Liz, so N = L - 19.
Now, let's use the second piece of information given. "In 4 years, the sum of Naida's age 7 years from now and Liz's age 11 years ago will be 5 more than the total."
In 4 years, Naida's age will be N + 4.
And Liz's age 11 years ago was L - 11.
The equation representing the given information is:
(N + 4) + (L - 11) = (N + L) + 5
Now, let's solve the equation to find their present ages.
Expanding the equation:
N + 4 + L - 11 = N + L + 5
Combining like terms:
N + L - 7 = N + L + 5
Simplifying the equation:
-7 = 5
This equation is not true. Therefore, there is no solution that satisfies the given conditions.