Simultaneous equation help

1. Mar 30, 2008

Paulo2014

1. The problem statement, all variables and given/known data
A zookeeper spends $133.10 altogether on bananas and nuts for the monkeys. He buys 8 kilograms more bananas than nuts. Bananas cost$2.20 per kilogram and nuts cost \$4.80 per kilogram.
How many kilograms of bananas did the zookeeper buy?
You must show the equations that you use to solve the problem.

3. The attempt at a solution

I think this has somthing to do with simultaneous equations but i don't know how to make them out of the question...
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Mar 30, 2008

happyg1

This is one of those problems that you need to read several times and write down the things that you know:
You know there are bananas (B) and nuts(N)
so the total is.......?
Then there are 8kg more B than N
so B+?=N.....
see if you can come up with a system from that.
You will be finding the total kg and dividing by the prices given.

3. Mar 30, 2008

Paulo2014

so would the first simutaneous equation be:

B+N=133.10?

4. Mar 30, 2008

happyg1

YEsssssss

5. Mar 30, 2008

Paulo2014

I don't see what the second one would be though... at a guess i would say it would be:

N+8=B

6. Mar 30, 2008

happyg1

Are there more Bananas or nuts? for the second one?

CC

7. Mar 30, 2008

Paulo2014

What do you mean by the same form?

8. Mar 30, 2008

happyg1

Well, for the first equation, you have
$$B+N=133.10$$
then for the second one (check my first post) you will have:
$$B+?=N$$
so you have B and N on the same side in the first equation, so you need the second equation to look like the first one in terms of where the B and N are. (also known in the nerdy math world as "standard form".)
CC

9. Mar 30, 2008

Paulo2014

So would that be B+N=133.10 and then you sub N=B+8 for the value of N so it looks like:

B+(B+8)=133.10?

i'm not sure...

10. Mar 30, 2008

happyg1

You're right. You got it.
Now you need to get your second equation to look like the first one...you need all letters on one side and the numbers on the other. Then you stack them on top of each other and there's your system.

11. Mar 30, 2008

Paulo2014

is the next step b^2=125.10?

12. Mar 30, 2008

happyg1

ok
You got:
$$B+N=133.10$$
B+(B+8)..not so much....

look, if N=B+8,(which is right)
and you want the N and B on the same side of the "=" sign, what do you need to do?
Forget the B+(B+8)..you are making this harder than it is meant to be.

13. Mar 30, 2008

Paulo2014

If the equation is B+8=N then you take N from both sides and take 8 from both sides so it would be B-N=-8

Is that right?

14. Mar 30, 2008

happyg1

PUrrrrfect!

15. Mar 30, 2008

Paulo2014

then do I go 2B=125.10

then B=62.55?

16. Mar 30, 2008

happyg1

yes yes
then to figure the kg, what?

17. Mar 30, 2008

Paulo2014

divide by 2.20?

18. Mar 30, 2008

happyg1

you got it!

19. Mar 30, 2008

happyg1

Now you have to do the Nuts!

20. Mar 30, 2008

Paulo2014

so the amount of bananas in kgs is 62.55/2.20=28.43 kgs (2dp)?

And the amount of nuts is 28.43/8=3.55 kgs?