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 be Jack's age.
Let y be Jen's age.
x = 2y - 2
x + 3y = 66
So:
2y - 2 + 3y = 66
5y - 2 = 66
5y = 68
y = 13.6.
So she's about 13 and a half years old.
Let's break down the problem step by step:
1. Let's assume Jack's current age is "x" and Jen's current age is "y".
2. According to the problem, Jack will be 2 years from being twice as old as Jen. This can be written as: x + 2 = 2(y + 2).
3. Simplifying the equation from step 2, we get: x + 2 = 2y + 4.
4. Subtracting 2 from both sides of the equation, we get: x = 2y + 2.
5. According to the problem, the sum of Jack's age and three times Jen's age is 66. This can be written as: x + 3y = 66.
6. Substituting the value of x from step 4 into equation 5, we get: (2y + 2) + 3y = 66.
7. Simplifying the equation from step 6, we get: 5y + 2 = 66.
8. Subtracting 2 from both sides of the equation, we get: 5y = 64.
9. Dividing both sides of the equation by 5, we get: y = 12.8.
However, age cannot be in decimal form, so we will round it down to the nearest whole number.
10. Therefore, Jen is 12 years old.
So, Jen is 12 years old.
To solve this problem, let's assign variables to the ages of Jack and Jen. Let's say Jack's age is J, and Jen's age is S.
According to the given information, "This Christmas, your brother Jack will be 2 years from being twice as old as your sister Jen." This can be written as:
J + 2 = 2(S + 2)
The second piece of information states that "The sum of Jack's age and three times Jen's age is 66." This can be written as:
J + 3S = 66
We now have a system of two equations:
J + 2 = 2(S + 2)
J + 3S = 66
To solve this system, we can start by simplifying the first equation:
J + 2 = 2S + 4
J = 2S + 2
Substitute this expression for J in the second equation:
(2S + 2) + 3S = 66
5S + 2 = 66
5S = 64
S = 64/5
S = 12.8
Since we can't have a decimal age, we round down to the nearest whole number. Therefore, Jen is 12 years old.