suzy is ten years older than Billy and next year she will be twice as old as Billy. How old is Suzy now? How old is Billy?
Billy is 9 and Suzy is 19
present age:
Billy -- x
Suzy -- x+10
next year:
Billy -- x+1
Suzy --- x+11 , but at that time she will be twice as old as Billy ---> x+11 = 2(x+1)
solve for x
To solve this problem, let's start by assigning variables to the ages of Suzy and Billy. Let's say Suzy's current age is S and Billy's current age is B.
According to the given information, Suzy is ten years older than Billy, so we can write the equation:
S = B + 10 (Equation 1)
It is also given that next year Suzy will be twice as old as Billy. So if we add 1 year to each of their ages, we can set up the equation:
S + 1 = 2 * (B + 1) (Equation 2)
Now we have two equations with two variables. We can solve the system of equations by substitution. We will substitute equation 1 into equation 2.
Substituting S from equation 1 into equation 2, we have:
B + 10 + 1 = 2 * (B + 1)
Simplifying the equation, we get:
B + 11 = 2B + 2
To solve for B, let's subtract B from both sides of the equation:
B + 11 - B = 2B - B + 2
11 = B + 2
Next, subtract 2 from both sides of the equation:
11 - 2 = B + 2 - 2
Simplifying, we have:
9 = B
So, Billy is 9 years old.
To find Suzy's age, we can substitute the value of B back into equation 1:
S = B + 10
S = 9 + 10
S = 19
Therefore, Suzy is 19 years old.