thebigunit said:
Im having a REAL hard time finding good links to math problems, specifically the word problem questions. Ones like:
This may or may not help, but here you go:
thebigunit said:
1. In 4 years time Angela will be twice as old as Barry and 4 times as old as Carol. 3 Years ago Angela was 3 times as old as Barry. How old are Angela, Barry, and Carol now?
Assign 'variables' to things that change in the problem, in order to make the statement work. In this problem, the age of 3 persons (Angela, Barry and Carol) will change. Lets call them x (Angela's age as of today), y (Barry's age as of today) and z (Carol's age as of today). It's just easier to write.
So, the problem says that in 4 years (add 4 to the current ages), Angela will be twice as old as Barry.
So,
x+4 = 2*(y+4)
Also, it says that in 4 years , Angela will be 4 times older than Carol, so:
x+4=4*(z+4)
The problem also says that 3 years ago (substract 3 to the current ages), Angela was 3 times older than Barry, so:
x-3=3*(y-3)
So you see, the variables of equation 1 and 3 are the same (x and y or Angela's and Barry's age as of Today)
Now, we need to isolate a common variable in those 2 equations. For a sake of ease, let's go with Angela's age, or x:
For equation 1, we get:
x= 2*(y+4)-4
For equation 3, we get:
x=3*(y-3)+3
Now, we can substitude x from equation 1 into equation 3:
2*(y+4)-4=3*(y-3)+3
Now, we need to do the same thing we did with Angela's age before (x) with Barry's age
: isolate it:
2y+8-4=3y-9+3
8-4+9-3=3y-2y
10=y
We know now that Barry's age as of today is 10.
We can go back to equation 1 or 3 and find Angela's age, by substituing Barry's, age in the equations. It doesn't matter which one you use, it will give you the same answer.
Let's use equation 1 (with Angela's age being isolated):
x= 2*(y+4)-4
x=2*(10+4)-4
x=2*(14)-4
x=28-4
x=24
We now know that Angela's age is 24. To prove that using eighter equation 1 or 3 doesn't matter, let's do the same thing with equation 3:
x=3*(y-3)+3
x=3*(10-3)+3
x=3*(7)+3
x=21+3
x=24
Now, using the second equation, we can find Carol's age as of today:
x+4=4*(z+4)
x+4=4z+16
x+4-16=4z
x-12=4z
(x-12)/4=z
z=(x-12)/4
z=(24-12)/4
z=(12)/4
z=3
So Carol's age is... 3!
There it is. As simple as that. The only way to succesfully do this kind of problem is by establising relationship (equations) between what's given (variables). Then, with these relationships, you can methodically and with logic find the answers. A little trick, in you have 3 variables, but only 2 equations, you will not be able to definately find a solid answer for all 3 variables. One of variable will be equal to a relationship that will depend on what the other 2 values of the variable are.