Max is 5 years older than Pauline. Next year he will be twice as old as she will be. How old is each now?
In one variable Pauline is x, while Max is x +5
One year later
Pauline is x + 1 while Max is x + 5 + 1
But he will be twice as old as she will be, so you multiply her future age by 2 to get it up to his age
2(x + 1) = x + 5 + 1
Solve for x and you have Pauline's age : )
Let's assign variables to Max's and Pauline's ages. Let M be Max's current age and P be Pauline's current age.
According to the problem, Max is 5 years older than Pauline, so we can write the equation: M = P + 5.
Next year, Max will be M + 1 years old, and Pauline will be P + 1 years old. The problem states that Max will be twice as old as Pauline, so we can write the equation: M + 1 = 2(P + 1).
Now we have a system of two equations:
1) M = P + 5
2) M + 1 = 2(P + 1)
From equation 1), we have M = P + 5. We can substitute this expression for M into equation 2) to solve for P:
(P + 5) + 1 = 2(P + 1)
P + 6 = 2P + 2
P - 2P = 2 - 6
-P = -4
P = 4
Now we know that Pauline is currently 4 years old. We can substitute this value into equation 1) to find Max's age:
M = P + 5
M = 4 + 5
M = 9
Therefore, Max is currently 9 years old and Pauline is currently 4 years old.
To find the ages of Max and Pauline, let's assign variables to represent their ages.
Let's say Max's age is represented by the variable "M" and Pauline's age is represented by the variable "P".
According to the information given, Max is 5 years older than Pauline. We can write this as:
M = P + 5
Next, it states that next year, Max will be twice as old as Pauline will be. Since we know that one year from now, both Max and Pauline will be one year older, we can write:
(M + 1) = 2(P + 1)
Now, we have two equations:
M = P + 5
(M + 1) = 2(P + 1)
To solve this system of equations, we can use the substitution method. Substitute the value of M from the first equation into the second equation:
((P + 5) + 1) = 2(P + 1)
Simplifying the equation:
P + 6 = 2P + 2
Rearranging the equation by subtracting P from both sides:
6 = P + 2
Subtracting 2 from both sides:
4 = P
Now, we can substitute the value of P back into the first equation to find Max's age:
M = 4 + 5
M = 9
Therefore, Pauline is 4 years old and Max is 9 years old.