Paulo is 6 years older than her sister. In 10 years, the sum of their ages be 50. Find their present ages.
Now:
sister's age --- x
Paulo's age --- x+6
10 years from now:
sister's age = x+10
Paulo's age = x+6 + 10 = x+16
x+6 + x+16 = 50
carry on...
To solve this problem, let's assign variables to the ages of Paulo and her sister.
Let P represent Paulo's present age, and S represent her sister's present age.
From the given information, we can deduce two equations:
1. "Paulo is 6 years older than her sister" can be written as: P = S + 6.
2. "In 10 years, the sum of their ages will be 50" can be written as: (P + 10) + (S + 10) = 50.
Let's rewrite equation 2 in terms of P and S:
P + 10 + S + 10 = 50
P + S + 20 = 50
Now, substitute equation 1 into equation 2:
(S + 6) + S + 20 = 50
2S + 26 = 50
Next, isolate the variable S by subtracting 26 from both sides:
2S = 24
Finally, divide both sides of the equation by 2 to solve for S:
S = 12
Now substitute the value of S into equation 1 to find P:
P = 12 + 6
P = 18
Therefore, Paulo's present age is 18, and her sister's present age is 12.