Question

Can someone please help me to answer this math question? Please? I will fan and give a medal...

Answer 1

Type A cream is 18% butterfat and type B cream is 24% butterfat. Set up a table to help you determine how many quarts of each type of cream must be used to create a 90 quart mixture that is 22% butterfat.

Answer 2

these are the steps I did --
30a+60b
-------------- = 0.22
90
30*(0.18)+60*(0.24)
------------------------------- = 0.22
90

Answer 3

this is what my teacher said was wrong-
I don't see the table.

--
I don't know what she means with the table..

Answer 4

30 and 60 quarts is the correct answer

Answer 5

30 of A and 60 of B.

Answer 6

okay, but how do I put that in a table like she wants?

Answer 7

We, first, there is no way you got 30 and 60 without doing some other math. Where did those numbers come from?

Answer 8

I'd do this instead:

A (qts) | B (qts) | A*0.18 | B*0.24 | C/90
------+-----+-------+------+-----
0 | 90 | 0 | 21.6 | (0+21.6)/ 90 = 0.24

and keep fillling in the table until you find reach the answers.

Answer 9

wait wait so how do I do that? @mjdennis ?

Answer 10

Where did 30 and 60 come from?

Answer 11

Good question

I got that answer by solving simultaneous equations . The poster seemed to dream it up!!

Answer 12

no sir/ma'am my sister told me to use 30 and 60... she didn't really tell me how to do it

Answer 13

OK, I'll take that for a start. You should not have tried to fool your teacher by giving your sisters answer, however.
So, you need two measurements that add up to 90 quarts. "qts" is short for quarts.
Start in the very first row with zero for cream A
Second column in the row has to be a number, that added to our choice for A, gets us to 90. So the second column is 90.
Skip the third column, we will come back.
Column four: Do you know how to figure out the _amount_ of fat in cream B, when you know the _amount_ of cream and the _percent_ of fat (18%)

Answer 14

so just forget about the 30 and 60 for now? or add the 30 into the first row?

Answer 15

You we not supposed to get 30 and 60 without attempting the problem, so of course forget about them for now.

Answer 16

Sorry, "You were not..."

Answer 17

When you get to the fourth row of the table, yeah, maybe you will have figured out that 30 and 60 work, but right now we need you to be able to figure out the missing items in all the empty spaces.

So again, do you know how to figure out the _amount_ of fat in cream B, when you know the _amount_ of cream (90 qts) and the _percent_ of fat (18%) ?

A (qts) | B (qts) | A*0.18 | B*0.24 | C/90
------+-----+-------+------+-----
0 | 90 | 0 | |
10 | | 1.8 | |
20 | | | |
30 | | | |

Answer 18

A (qts) | B (qts) | A*0.18 | B*0.24 | C/90
------+-----+-------+------+-----
0 | 90 | 0 | |
10 | | 1.8 | |
20 | | 3.6 | |
30 | | 5.4 | |

Answer 19

so like this?

Answer 20

Yes. But I really want you to work one row across at a time, that way the _method_ can stick with you for tougher problems.

Can you find the value for the first row, in the first blank column (the one marked "B*0.24")?

Answer 21

would that be 0? like the other two?

Answer 22

No.
We are going to take a step backwards so you know how to do this.
What is the value of B in the first row. Just B.

Answer 23

90

Answer 24

Right. That is 90 quarts of cream B. 24% of that is fat. So how many quarts of fat come in 90 quarts of cream B?

Answer 25

oh when you said find the value of "B*0.24" did you want me to do this..
90*0.24=21.6

Answer 26

Exactly! Sorry that my shortcut was not clear.

Answer 27

So the final stem in each row is to ad the entries in the 3rd and fourth columns, and divide by the total 90 quarts, to find the percentage of fat in the mix.
this first one is too easy, because it is (0+21.6)/90 = 21.6/90 = 24%, but we knew that.

Answer 28

If that makes sense, try filling in the second row.
Now A isn't zero, it is 10 quarts.
So B is 10 less than the total of 90, or 90-10=80.
Can you get the rest of the second row and check back with me?

(You should show your teacher that you did a sensible approach to solving the table, that is why I am having you count by tens instead of jumping straight to 30.)

Answer 29

ok I'll try it

Answer 30

I've got about 5 minutes before I have to go offline? Do you want me to check anything?

Answer 31

@mjdennis yes sir sorry it took so long...

Answer 32

A qts | B qts | A*0.18 | B*0.24 | C/90
--------- + ---------- + ----------- + -----------+ ----------
0 | 90 | 0 | 21.6 | 24%
10 | 80 | 1.8 | 19.2 | 23%
20 | 70 | 3.6 | 16.8 | 0.226666666
30 | 60 | 5.4 | 14.4 | 22%

Answer 33

Looks good! Hope you can apply this method to other problems.

If you overshoot the answer, say you had been counting by 20s and missed that 22%, you can go back and put some new answers..

Answer 34

okay! Thank you so much!! you are very helpful!!