Sam is one-third as old as his brother. In six years Sam will be one-half as old. How old is Sam now?
S = Present Sam's age
B = Present brother's age
Sam is one-third as old as his brother mean:
S = B / 3
After six year Sam will be S + 6 years od.
Brother will be B + 6 years old.
In six years Sam will be one-half as old mean:
( S + 6 ) / ( B + 6 ) = 1 / 2
Now you must solve system of 2 equations with 2 unknows:
S = B / 3
( S + 6 ) / ( B + 6 ) = 1 / 2
Try solve this.
The solutions are :
S = 6 years old
B = 18 years old
Proof:
S = B / 3 = ( 1 / 3 ) B
S / B = 6 / 18 = 6 / ( 6 * 3 ) = 1 / 3
( S + 6 ) / ( B + 6 ) = ( 6 + 6 ) / ( 18 + 6 ) = 12 / 24 = 12 / ( 12 * 2 ) = 1 / 2
Pat had 5 snowballs less than Sam
To solve this problem, we need to set up equations based on the given information. Let's use S to represent Sam's current age and B to represent his brother's current age.
From the given information, we know that Sam is one-third as old as his brother, so we can write the equation:
S = (1/3)B
We also know that in six years, Sam will be one-half as old as his brother, which can be represented as:
S + 6 = (1/2)(B + 6)
Now we can solve these equations to find Sam's age. We'll substitute the first equation into the second equation:
(1/3)B + 6 = (1/2)(B + 6)
To get rid of the fractions, let's multiply both sides of the equation by 6:
2B + 36 = 3(B + 6)
2B + 36 = 3B + 18
Rearranging the equation:
2B - 3B = 18 - 36
-B = -18
Now, multiplying both sides by -1 to solve for B:
B = 18
Substituting this value of B back into the first equation:
S = (1/3)(18)
S = 6
Therefore, Sam is currently 6 years old.