Question 638396: John's age is 3 years more than twice Bill's age. Three years ago John was 4 times as old as Bill was then. How old is Bill now?
Answer by josh_jordan(263)   (Show Source):
You can put this solution on YOUR website! To make things easier, let's use the letter J to represent John's age, and the letter B to represent Bill's age. The first sentence states that John is 3 years more than twice Bill's age. In other words:
J = 2B + 3
Now let's look at the second sentence, which states three years ago John was 4 times as old as Bill was then. In other words:
J - 3 = 4(B - 3)
Now that we have our 2 equations (J=B+3 and J-3=4(B - 3)), we can solve. Since we know John's age in terms of Bill, we will substitute 2B + 3 for our second equation:
2B + 3 - 3 = 4(B - 3)
The left side of our equation is now 2B and the right side is still 4(B - 3). Using the distributive property, we will multiply the 4 by what's inside of the parenthesis: 4B - 12. Our equation now looks like
2B = 4B - 12
We need to get the B's on one side of the equal sign, so we will subtract 2B from both sides, which gives us 0 = 2B - 12. We will then add 12 to both sides, giving us 12 = 2B. To get the B by itself, we will divide both sides by two, which will give us Bill's age: 6 = B. So, Bill is 6 years old.
To find out John's age, replace the B in the first equation with 6:
J = 2(6) + 3
J = 12 + 3
Therefore, John is 15
Final Answer: John is 15 and Bill is 6
|
|
|
