Adam is 5 years younger than Eve. In 1 year, Eve will be three times as old as Adam was 4 years ago. Find their ages now.
at present time:
Eve---- x years
Adam --- x-5 years
one year from now, Eve will be x+1
four years ago Adam was x-5 - 4 = x-9
x+1 =3(x-9)
x+1 = 3x - 27
-2x = -28
x=14
so Eve is now 14 and Adam is 9
check:
one year from now Eve will be 15
four years ago Adam was 5
is 15 three times 5 ?? YES
Ah, the age-old question of Adam and Eve! Let's see if we can solve this riddle using our mathematical powers, shall we?
Let's assume Adam's current age is A, and Eve's current age is E.
According to the problem, we know that Adam is 5 years younger than Eve. So, we can write the equation: A = E - 5.
Now, in 1 year, Eve will be three times as old as Adam was 4 years ago. So, let's translate that into an equation: (A - 4) * 3 = E + 1.
We have two equations with two unknowns. Let's solve the system of equations:
Substituting the value of A from equation 1 into equation 2, we get (E - 5 - 4) * 3 = E + 1.
Simplifying that, we have (E - 9) * 3 = E + 1.
Expanding and simplifying the equation further, we have 3E - 27 = E + 1.
Bringing all the E terms to one side and the constants to the other side, we get 3E - E = 1 + 27.
Simplifying that, we have 2E = 28.
Finally, we divide both sides by 2: E = 14.
Now, substituting this value of E into equation 1, we get A = 14 - 5.
Simplifying that, we have A = 9.
So, the present age of Adam and Eve is Adam: 9 years and Eve: 14 years.
Hope that brings a smile to your face!
Let's assume Adam's age is A and Eve's age is E.
According to the given information, Adam is 5 years younger than Eve:
A = E - 5 ---(Equation 1)
In 1 year, Eve will be three times as old as Adam was 4 years ago:
(E + 1) = 3(A - 4) ---(Equation 2)
Now, we can solve these two equations to find their ages:
Substituting Equation 1 into Equation 2:
(E - 5 + 1) = 3(A - 4)
(E - 4) = 3(A - 4)
(E - 4) = 3A - 12
E - 3A = -12 + 4
E - 3A = -8 ---(Equation 3)
Now, we have two equations:
A = E - 5 ---(Equation 1)
E - 3A = -8 ---(Equation 3)
We can substitute Equation 1 into Equation 3:
(E - 3(E - 5)) = -8
(E - 3E + 15) = -8
15 - 2E = -8
-2E = -8 - 15
-2E = -23
E = (-23) / (-2)
E = 11.5
Now, we can substitute the value of Eve's age (E) into Equation 1 to find Adam's age:
A = E - 5
A = 11.5 - 5
A = 6.5
Therefore, Adam is currently 6.5 years old and Eve is currently 11.5 years old.
To solve this problem, we'll set up equations based on the given information.
Let's assume Eve's current age is E, and Adam's current age is A.
From the first sentence, we know that Adam is 5 years younger than Eve. So, we can write the equation:
A = E - 5
From the second sentence, we know that in 1 year, Eve will be three times as old as Adam was 4 years ago. This can be written as:
(E + 1) = 3 * (A - 4)
Now, we have a system of two equations with two variables:
A = E - 5 -- (Equation 1)
(E + 1) = 3 * (A - 4) -- (Equation 2)
We can use substitution or elimination to solve this system of equations. Let's substitute Equation 1 into Equation 2:
(E + 1) = 3 * ((E - 5) - 4)
E + 1 = 3 * (E - 9)
E + 1 = 3E - 27
2E = 28
E = 14
Now that we have found Eve's age (E = 14), we can substitute it back into Equation 1 to find Adam's age:
A = 14 - 5
A = 9
Therefore, Eve is currently 14 years old, and Adam is currently 9 years old.