Question 386672: Tom is 4 times as old as Todd. In 7 years Tom's age will be 5 years less than 3 times as old as Todd. How old is Todd?
Answer by gwendolyn(128)   (Show Source):
You can put this solution on YOUR website! let x=Tom's age
let y=Todd's age
Tom is 4 times as old as Todd. This can be translated into an equation:
x=4y
In 7 years, Tom will be 5 years younger than three times Todd's age. This means that when both Todd's age and Tom's age are 7 years greater, Todd's age times three minus 5 will be equal to Tom's age. Since the variables x and y represent Tom's and Todd's current ages, their ages in 7 years can be expressed as (x+7) and (y+7). So, the equation looks like the one below:
(x+7)=3(y+7)-5
First, we'll distribute the three over the second set of parentheses.
(x+7)=3y+21-5
The parentheses around x+7 are unnecessary, so they can be deleted. The two terms in the second half of the equation which have no variables can be combined.
x+7=3y+16
Now, we can substitute the value of x in terms of y from the first equation into the second.
x+7=3y+16
4y+7=3y+16
Now, we can subtract 3y from both sides of the equation.
4y+7=3y+16
4y+7-3y=3y+16-3y
y+7=16
Finally, we subtract 7 from both sides to find y.
y=9
The equation asks for Todd's age, which y represents. Therefore, Todd's age is 9.
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