When Lee was thrice as old as Kevin, his sister Kate was twenty seven. When Kevin was half as old as Kate, then brother Lee was thirty eight. Their ages add to one forty three. How old are Kevin, Kate, and Lee?
if their ages now are Lee,Kevin,Kate = x,y,z,
a years ago, Kate was 27
b years ago, Lee was 38
x+y+z = 143
x-a = 27
z-a = 3(y-a)
x-b = 38
2(y-b) = z-b
Now just solve for x,y,z
It might be easier to eliminate a and b first, so you just have 3 equations to solve.
Let's assign variables to the unknowns:
Let's say Kevin's age is "x."
Lee's age would then be "3x" since Lee was thrice as old as Kevin.
And Kate's age would be "27" since when Lee was thrice as old as Kevin, Kate was twenty-seven.
Now let's work on the second part of the problem. When Kevin was half as old as Kate, brother Lee was thirty-eight.
So, Kevin's age would be (1/2) * Kate's age.
And Lee's age would be Kate's age plus eleven more years.
Now we can form equations based on the given information:
x + 3x + 27 + 38 + (1/2) * Kate's age + Kate's age + 11 = 143
Combine like terms:
4x + (3/2) * Kate's age + 76 = 143
Rearrange the equation:
4x + (3/2) * Kate's age = 143 - 76
4x + (3/2) * Kate's age = 67
Since the total sum of their ages is 143, we can write another equation:
x + 3x + 27 + 38 + Kate's age + 11 = 143
Combine like terms:
4x + Kate's age = 143 - 27 - 38 - 11
4x + Kate's age = 67
Now we have a system of equations where:
4x + (3/2) * Kate's age = 67
4x + Kate's age = 67
Let's solve this system of equations to find the values of x and Kate's age.
Subtract the second equation from the first equation:
(4x + (3/2) * Kate's age) - (4x + Kate's age) = 67 - 67
(3/2) * Kate's age - Kate's age = 0
(3/2 - 1) * Kate's age = 0
(1/2) * Kate's age = 0
Since (1/2) * Kate's age = 0, Kate's age must be 0.
Substitute Kate's age as 0 into any of the equations:
4x + 0 = 67
4x = 67
x = 67/4
x = 16.75
Therefore, Kevin's age is approximately 16.75 years old.
With Kevin's age, we can find Lee's age:
Lee's age = 3 * Kevin's age
Lee's age = 3 * 16.75
Lee's age = 50.25
And since we know Kate's age was 27, we can check if the sum of their ages equals 143:
Kevin + Kate + Lee = 16.75 + 27 + 50.25 = 94
The sum is not 143 as given in the problem, which means there is an error in the given information or the problem cannot be solved as stated.
To solve this problem, let's assign variables to the ages of Kevin, Kate, and Lee.
Let's say Kevin's age is K, Kate's age is C, and Lee's age is L.
According to the given information:
1) "When Lee was thrice as old as Kevin, his sister Kate was twenty-seven."
So, at that time, Lee's age was 3K and Kate's age was 27.
2) "When Kevin was half as old as Kate, then brother Lee was thirty-eight."
So, at that time, Kevin's age was C/2 and Lee's age was 38.
3) "Their ages add to one hundred forty-three."
So, we have the equation K + C + L = 143.
Now, we can use these equations to solve for the ages of Kevin, Kate, and Lee.
Using equation 1, we can substitute Lee's age with 3K:
3K = 27
Divide both sides of the equation by 3:
K = 9
Using equation 2, we can substitute Lee's age with 38:
C/2 = 38
Multiply both sides of the equation by 2:
C = 76
Now, we can substitute the values of K and C into equation 3 to solve for Lee's age:
9 + 76 + L = 143
Combine like terms:
85 + L = 143
Subtract 85 from both sides of the equation:
L = 58
Therefore, Kevin is 9 years old, Kate is 76 years old, and Lee is 58 years old.
Answer:
Lee = 57
Kevin = 35
Kate = 51
Is this right?