john is three times as old as Greg, and Greg is half the age of Bob, Steve is two times the age of John and Bob combined. if Steve's age is 60, how old is Greg's older cousin Jane, who is two years older than Greg?
j = 3g
g = b/2
s = 2(j+b)
s = 60
solving those, we get Greg is 6.
So, Jane is 8.
Well, this is quite the age-related puzzle! Let's break it down into some clown-approved equations:
Let's say Greg's age is G.
Since John is three times as old as Greg, John's age is 3G.
And if Greg is half the age of Bob, Bob's age is 2G.
Now, we know Steve is two times the age of John and Bob combined, which means Steve is 2(3G + 2G) = 2(5G) = 10G.
If we know that Steve's age is 60, we can set up an equation: 10G = 60.
Solving for G, we find that G = 6.
Therefore, Greg is 6 years old.
Since Greg's older cousin Jane is two years older than Greg, Jane is 6 + 2 = 8 years old.
So, Greg's older cousin Jane is 8 years old. I hope that puts a smile on your face!
Let's break down the information given step by step:
1. John is three times as old as Greg.
Let's say Greg's age is x. Then John's age is 3x.
2. Greg is half the age of Bob.
Let's say Bob's age is y. Then Greg's age is y/2.
3. Steve is two times the age of John and Bob combined.
Steve's age is given as 60. So, 3x + y + y = 60.
Simplifying this equation, we get 4x + y = 60.
4. If Jane is two years older than Greg, her age would be y + 2.
Now, we can solve for x and y:
From equation 4: Jane's age = y + 2
From equation 2: Greg's age = y/2
From equation 1: John's age = 3x
Since Steve's age is 60, we can substitute the values derived above into equation 3 to solve for x and y:
4x + y = 60
Replacing Jane's age with y + 2:
4x + (y + 2) = 60
Substituting Greg's age from equation 2:
4x + (2y) + 2 = 60
Now, we have two equations with two variables:
4x + 2y = 58 ----(Equation 5)
To solve for x and y, we need another equation. Let's go back to equation 1:
John is three times as old as Greg, so 3x = x + 2y.
Now, we have two equations:
3x = x + 2y ----(Equation 6)
We can solve these two equations simultaneously to find the values of x and y.
By subtracting x and 2y from both sides of Equation 6, we get:
2x - 2y = 0,
or
2x = 2y.
By dividing both sides by 2, we find:
x = y.
Now, we can substitute the value of y in Equation 6:
3y = y + 2y.
Simplifying this equation:
3y = 3y.
This implies that y can be any value, as long as it's a real number.
So, we do not have enough information to determine the exact ages of Greg and Jane.
To find the age of Greg's older cousin Jane, we need to calculate the ages of Greg, John, and Bob first.
Let's assign variables:
Greg's age = G
John's age = J
Bob's age = B
Steve's age = S
Jane's age = JG (since Jane is two years older than Greg)
We know that:
1) John is three times as old as Greg: J = 3G
2) Greg is half the age of Bob: G = 0.5B
3) Steve is two times the age of John and Bob combined: S = 2(J + B)
4) Steve's age is given as 60: S = 60
Now, let's solve the equations to find the values of G, J, and B:
From equation 3, substitute J = 3G and B = 2G into equation 2:
S = 2(3G + 2G)
60 = 2(5G)
Divide both sides by 2:
30 = 5G
G = 6
Now that we know Greg's age (G = 6), we can find John's age (J) and Bob's age (B):
J = 3G = 3(6) = 18
B = 0.5G = 0.5(6) = 3
Since we have Greg's age, we can now find Jane's age (JG):
JG = G + 2 = 6 + 2 = 8
Therefore, Greg's older cousin Jane is 8 years old.