Re: "Age" Word Problem
Hello vonsmiley
vonsmiley said:
I was wondering if some one can help me with this problem I'm in trouble from the set up
The problem says: The barn on Sue's small farm was built 10 years before the garden shed and twenty years after the house. Twenty years ago, the age of the house was the same as the combined ages of the barn and the garden shed. What is the present age of each building?
Barn Shed house
if the shed is 'x' and the barn is x-10 what is the relationship with the shed and the house, if the barn and the house are (x-10) + 20? or is all that wrong? I don't know what I'm doing!
Alright we will call the shed \(\displaystyle \L\bold x\), the barn \(\displaystyle \L\bold y\) and the house \(\displaystyle \L\bold z\).
1)The barn on Sue's small farm was built 10 years before the garden shed: \(\displaystyle \L\bold y=x-10\)
2)The barn on Sue's small farm was built twenty years after the house: \(\displaystyle \L\bold y=20+z\)
3) Twenty years ago, the age of the house was the same as the combined ages of the barn and the garden shed: \(\displaystyle \L\bold z=y+x\)
Notice that my first 2 equations have the same variable except \(\displaystyle \L\bold z\). So that means we should use that as our system to start off. Now we need to find out what the z is in terms of x and y. Well I worked it out and this is what I get.
\(\displaystyle \L\bold y=20+z\)
\(\displaystyle \L\bold y=20+y+x\)
\(\displaystyle \L\bold 0=20+x\)
Since filling \(\displaystyle \L\bold x+y\) in for \(\displaystyle \L\bold z\) yields \(\displaystyle \L\bold y\), we can eradicate that. But we do have another way to solve this. We can change the \(\displaystyle \L\bold x\) in terms of \(\displaystyle \L\bold y\) and \(\displaystyle \L\bold z\). So we use our third equation: \(\displaystyle \L\bold z=y+x\) to find what \(\displaystyle \L\bold x\) equals in our third equation \(\displaystyle \L\bold y=x-10\) since the former did not work.
\(\displaystyle \L\bold x=z-y\)
So fill that into our original first equation:\(\displaystyle \L\bold y=z-y-10\)
Now we use are other equation that is equal to y and has the terms of \(\displaystyle \L\bold y\) and \(\displaystyle \L\bold z\) to solve a system.
\(\displaystyle \L\bold y=z-y-10\)
\(\displaystyle \L\bold y=20+z\)
So since both are equal to \(\displaystyle \L\bold y\), set them equal to each other making:
\(\displaystyle \L\bold z-y-10=20+z\)
Simplify this to get to \(\displaystyle \L\bold y\) (barn age). If you get a negative answer, make it positive since time cannot be negative. The reason you might get one is because people can interpret this statement conversely "the barn on Sue's small farm was built 10 years before the garden shed" by making the garden shed age=barn age+10yrs, thus making a positive answer.
Once you get \(\displaystyle \L\bold z\) you can get the \(\displaystyle \L\bold x\) and \(\displaystyle \L\bold y\) by filling them back into our equations (if you get get \(\displaystyle \L\bold z=-1\), which it is not, then put \(\displaystyle \L\bold 1\) in for \(\displaystyle \L\bold z\) not \(\displaystyle \L\bold-1\)).
Can you finish :?:
