How Many Kilograms of Bananas Did the Zookeeper Buy?

[Paulo2014]

Homework Statement

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.

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...

 

[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.

 

[Paulo2014]

so would the first simutaneous equation be:

B+N=133.10?

 

[happyg1]

YEsssssss

 

[Paulo2014]

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

N+8=B

 

[happyg1]

Are there more Bananas or nuts? for the second one?
I had to reread the question. Sorry for the edit.

CC

 

[Paulo2014]

What do you mean by the same form?

 

[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

 

[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...

 

[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.

 

[Paulo2014]

is the next step b^2=125.10?

 

[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.

 

[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?

 

[happyg1]

PUrrrrfect!

 

[Paulo2014]

then do I go 2B=125.10

then B=62.55?

 

[happyg1]

yes yes
then to figure the kg, what?

 

[Paulo2014]

divide by 2.20?

 

[happyg1]

you got it!

 

[happyg1]

Now you have to do the Nuts!

 

[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?

 

[happyg1]

you lost ME there.
What did you get for the N when you solved for it?
Why divide by 8?
I got 28.43 for Bananas...

 

[Paulo2014]

I got 3.55 kgs for nuts as the question says there is 8 times as many bananas than nuts... Is that not right?

 

[happyg1]

As the question is stated, the zookeeper buys 8 MORE kg, not 8 TIMES more
Go back to your original equations and plug in there

 

[Paulo2014]

so its 20.43 kgs of nuts?

 

[happyg1]

you had:
B+N=133.10
you solved for B and you got
125.10
HOW can you get N from that?

 

[Paulo2014]

133.10-125.10
=8kg... doesn't seem right...

 

[HallsofIvy]

I really hate it when people do stuff like "bananas (B) and nuts(N)". B and N are numbers, not "bananas" or "nuts". Often it doesn't make any difference but here- are B and N the weight, in kg, of bananas and nuts bought or the amount of money, in dollars, paid for them?

The first equation you give, and happyg1 approves, is B+N=133.10, apparently from "A zookeeper spends $133.10 altogether on bananas and nuts". Since 133.10 is dollars, I must presume that "B" is the amount spent on bananas and "N" the amount spent of nuts.

And then you give "N+8=B", apparently from "He buys 8 kilograms more bananas than nuts". Which means you are taking "N" and "B" now to be weight in kg.

You can't have it both ways! I'm sorry but it looks to me like happyg1 is leading you down the wrong path.

Start by stating explicitely what your letters stand for: N= weight of nuts bought in kg, B= weight of bananas bought in kg. Now you can say: B= N+ 8.

Since "Bananas cost $2.20 per kilogram and nuts cost $4.80 per kilogram", B kg of bananas will cost 2.20B dollars and N kg of nuts will cost 4.80N. B kg of bananas and N kg of nuts will cost 2.20B+ 4.80N dollars and we are told that the zookeeper spent 133.10 dollars total: 2.20B+4.80N= 133.10.

Your two equations are B= N+ 8 and 2.20B+ 4.80N= 133.10.

 

[drpizza]

I agree with HallsofIvy. I'd be surprised if your teacher didn't say that the very first step on these problems is defining the variables. Before you even write the first equation, you should have something like:

Let B = the weight in kilograms of bananas
N = the weight in kilograms of nuts


Defining your variables helps reduce the likelihood of making the mistake that was already made.

 

[happyg1]

Hey guys,
I agree with you. I missed the kg vs. weight. I teach students who are struggling with math and this problem looked a lot like ones that we had, except for the "dual" units.
I apologize for the errors in my posts. We just did 50 problems, they were all single units..."zoo guy buys a total of 150 bananas and apples. He bought 30 more bananas than apples. How many bananas and apples did he buy? "
Those are the problems that we are doing. NOT like this problem.
not dealing with cost/kg, just cost, or kg (well, here we do pounds...kgs are too strange.)
Halls and pizza are correct. I missed it and I should have been more astute when I read the problem...and A LOT MORE PRECISE when I responded.
As always, Halls is correct.:)
again, forgive my error.
CC

 

[Paulo2014]

Um...

 

[HallsofIvy]

Um what? Have you solved the two equations B= N+ 8 and 2.20B+ 4.80N= 133.10?
Since B= N+8, replace the B in the second equation with that: 2.20(N+ 8)+ 4.80N= 133.10. Now solve that equation for N.