Question

15. A restaurant has one type of milk that has 2% fat and another that has 7% fat. how many quarts of each type does the restaurant need to make 40 quarts of a milk mixture that is 5% fat?

a. 24 quarts of the 2% milk and 16 quarts of the 7% milk
b. 16 quarts of the 2% milk and 24 quarts of the 7% milk
c. 16 quarts of the 2% milk and 16 quarts of the 7 milk
d. 24 quarts of the 2% milk and 24 quarts of the 7% milk

Answer 1

oh boy a mixture problem ...

Answer 2

@dtan5457

Answer 3

yeah o_o

Answer 4

lets call the amount of 7% milk x so the amount of 2% milk is \(40-x\) because the total is 40

Answer 5

\(5\% \) of \(40\) is \(2\) right?

Answer 6

that means
\[0.07x+0.02\times (40-x)=2\] or to make it easier
\[7x+2(40-x)=200\]

Answer 7

O_O I-I think

Answer 8

well this is how i did it..

x+y=40

2x+7y/40=5

2x+7y=200

x=40-y

plug in to get

80-2y+7y=200

5y=200

y=24
x=16

b. 16 quarts of the 2% milk and 24 quarts of the 7% milk

Answer 9

yeah it is because ten percent of forty is four, so five percent is two

Answer 10

@satellite73

please check my work

Answer 11

wait nvm i already screwed up 5y=120

Answer 12

not 200..

Answer 13

o.o

Answer 14

at some point you are going to have to solve \[7x+2(40-x)=200\]

Answer 15

wow wow wow wow wow wow wow wow wow wow. now I gotta read all of this

Answer 16

yes! @Mimi_Styles
TO understand IT!!!

Answer 17

if i just solve for y for 7% milk, isn't that enough?

Answer 18

ok we can start again if you like and do it slow

Answer 19

these problems are all more or less the same
do one or two and you can do them all

Answer 20

<____>

Answer 21

i don't know if that is a yes or a no

Answer 22

i just wanna know if i my answer is correct so i can rest in peace

Answer 23

I made this face and it's called the confused face

Answer 24

ok first off, do you know that \(7\%\) means \(.07\)

Answer 25

yes.

Answer 26

and do you know that 7 percent of a number means that number times \(.07\) ?

Answer 27

if you do not, feel free to say "i know it now"

Answer 28

I know now... ._.

Answer 29

ok
so for example 7% of 50 is \(.07\times 50\) and 7% of \(x\) is \(.07x\)

Answer 30

o.o

Answer 31

good to here?

Answer 32

ohh okay

Answer 33

if we are gong to solve one of these, we have to have a variable
some people actually like two variables, i think that is more confusing, one will do
and we have to say what it is
i say "let \(x\) be the amount of 7% milk"

Answer 34

then in terms of \(x\) we know that the total number of gallons is 40
if \(x\) of them are 7% milk the rest, the 2% milk is \(40-x\)
for example if there were 15 gallons of 7% milk there would have to be \(40-15=25\) gallon of 2% milk

Answer 35

since we now know that 7% of x is \(.07x\) and also that 2% of \(40-x\) is \(.02(40-x)\) we can make an equation

Answer 36

the total amount of fat or whatever is 5% of 40, which we decided is 2
that means
\[.07x+.02(40-x)=2\]

Answer 37

o.o ohh

Answer 38

now that is somewhat annoying to solve

Answer 39

but not too bad if you multiply both sides by 100 and solve
\[7x+2(40-x)=200\]

Answer 40

i am sure you can do that one
once you get it, you will have the amount of 7% milk

Answer 41

uhhh D:

Answer 42

wait wait *lost*

Answer 43

what step

Answer 44

"but not too bad if you multiply both sides by 100 and solve
7x+2(40−x)=200 " <----

Answer 45

that one.

Answer 46

\[.07x+.02(40-x)=2\] is what needs to be solved
and you can do it with the decimals in place if you like

Answer 47

but multiplying by 100 moved the decimal over two places, i.e. gets rid of them

Answer 48

if you multiply by 100 you have to multiply both decimals by 100 to get rid of the decimal, but you also have to multiply 2 by 100 to get 200
that is why \[.07x+.02(40-x)=2\] is the same as \[7x+2(40-x)=200\]

Answer 49

ohh~

Answer 50

ohhh! ^_^

Answer 51

so what im doing is...multiplying each sides by 100 ?

Answer 52

yes to get from the equation with decimals to the equation with out them
you still have to solve it though

Answer 53

0.02 x + 0.07(40 -x ) =40(0.05)

2x + 280-7x = 200
-5x =-80
x = 16
fat = 40-16 = 24

Answer 54

ok looks reasonable

Answer 55

i am not sure how you got that one, but it is correct also

Answer 56

o.o

Answer 57

wait so 16 2% and 24 7%?

Answer 58

yes

Answer 59

@Mimi_Styles switched them

Answer 60

\[0.02 x + 0.07(40 -x ) =40(0.05) \] has \(x\) as the 2% milk

Answer 61

btw "whole milk" is about \(3.25\%\) or so
not 5% and certainly not 7%

Answer 62

oooohhh