Question

Hanna makes her own furniture polish using twenty-five percent vinegar and seventy-five percent olive oil. Write and solve an equation to determine how much total solution she made if she used 2 cups of vinegar. Show your work

Answer 1

OK. So what problem are you having with this?

Answer 2

i need help with the equation

Answer 3

Well, you are given some numbers and variables. What can you get out of the paragraph for those?

Answer 4

25% vinegar, 75% olive oil, and 2 cups of solution

Answer 5

So, we can use v for vinegar and o for olive oil, but I see a mistake there. It is not 2 cups of solution. It is 2 cups of vinegar and the question asks for how much solution.

Answer 6

oh sorry

Answer 7

np. Now, you need the %s in decimal. So, can you do an equation with that?

Answer 8

in decimal form you mean?

Answer 9

.25v + .75o

Answer 10

Yah. That works.
.25v + .75o = some total. But the total is 100%.

.25v + .75o = 1

Answer 11

OK. That is an equation in two unknowns. But they give you another fact, the 2 cups.

So... hmm... might be easier to do this as a ratio and then add. Know how ratios work?

Answer 12

ya

Answer 13

0.75 : 2

Answer 14

Well... the 2 cups is of vinager.... so you would have to do the ratio a little different.

\(v:o\implies \)

\(.25:.75\)

Now what would the second ratio be with the 2 cups of vinegar and unknown olive oil?

Answer 15

\[o : 2\]

Answer 16

It needs to be in the same order. If v is first, then it must always be first. If o is first, it must always be first. =) The order you pick is up to you, but both equations must match.

Answer 17

\[o = 1.5\] i think

Answer 18

I bring that up because I did v first, and you did o first, which gets a wrong answer.

Answer 19

Ya it will

Answer 20

So, which do you want first? o or v?

Answer 21

o

Answer 22

o : v

Answer 23

OK:
\(o + v = ?\) and we know they use \(.75o + .25v = 1\) means we can do a ratio of: \(o:v\)

That implies:
\(.75:.25\) and your one...
\(o:2\)

Can you solve for o now?

Answer 24

i think o = 6?

Answer 25

Yes. o=6. So what does that make the total of oil and vinegar?

Answer 26

8

Answer 27

8 cups

Answer 28

=)

Answer 29

thx

Answer 30

Just to be clear, that .75o+.25v=1, I got that from percentages.

75% Oil + 25% Vinegar = 100% Solution

Some Amount of Oil + Some Amount of Vinegar = Some Amount of Solution lets me get the total for the solution.

That was what I used that told me that ratios might be best.

I hope that helps with other problems.

Answer 31

ok