Age Problem Solution with Algebra
The image contains a math word problem that reads:
"Richard and Tom have a combined age of 49. Richard is 3 years older than twice Tom's age. How old are Richard and Tom?"
Let's use algebra to solve this problem. We'll let R represent Richard's age and T represent Tom's age.
We have two pieces of information:
1. Combined age: R + T = 49
2. Richard's age in relation to Tom's age: R = 3 + 2T
Now we have two equations:
(1) R + T = 49
(2) R = 3 + 2T
We can substitute the value of R from equation (2) into equation (1):
3 + 2T + T = 49
Now combine like terms:
3 + 3T = 49
Subtract 3 from both sides to solve for T:
3T = 49 - 3
3T = 46
Now divide by 3 to get T:
T = 46 / 3
T = 15⅓
However, ages are typically represented in whole numbers so the age should not be a fraction. Let's check our calculation to avoid any fraction since the question probably expects whole numbers as an answer.
Dividing 46 by 3 again,
T = 46 / 3
T = 15 with a remainder of 1. This means that Tom's age is 15, not 15⅓.
Now we can find Richard's age by substituting T back into equation (2):
R = 3 + 2(15)
R = 3 + 30
R = 33
So, Richard is 33 years old and Tom is 15 years old.
