This Christmas,your brother Jack will be 2 years from being twice as old as your sister Jen.The sum of Jack's age and three times Jen's age is 66.How old is Jen?
Let x = Jack's age
Let y = Jen's age
From the information above:
2y = x - 2
x + 3y = 66
Get x on one side for the first equation.
x = 2y + 2
Substitute 2y + 2 for x in the second equation and solve for y. Put that value in the first equation to solve for x. Check by inserting both values into the second equation.
I hope this helps.
13.5
To solve this problem, we need to set up a system of equations based on the given information.
Let's denote Jack's current age as J and Jen's current age as S.
According to the first statement, Jack will be 2 years from being twice as old as Jen, which can be represented as:
J + 2 = 2(S + 2)
The "+2" represents the two years from now, and "2(S + 2)" indicates that Jack will be twice as old as Jen (S + 2) two years from now.
Simplifying the equation above, we have:
J + 2 = 2S + 4
Now let's move on to the second statement. The sum of Jack's age and three times Jen's age is 66, which can be written as:
J + 3S = 66
We now have a system of two equations:
J + 2 = 2S + 4 (equation 1)
J + 3S = 66 (equation 2)
To find the values of J and S, we can solve this system of equations using substitution or elimination method.
Using the substitution method, we can solve equation 1 for J:
J = 2S + 2
Now substitute this value of J into equation 2:
(2S + 2) + 3S = 66
5S + 2 = 66
5S = 66 - 2
5S = 64
S = 64/5
S = 12.8
Since ages are typically whole numbers, we can't have 12.8 as Jen's age. This indicates that there may be an error in the given problem statement or an assumption is made.
Please double-check the problem statement and provide any additional information if available.