A salsa recipe uses green pepper, onion, and tomato in the extended ratio 2 : 5 : 8. How many cups of onion are needed to make 105 cups of salsa?

Question

shaleiah · Answer

@Michele_Laino

jhonyy9 · Answer

green pepper          onion          tomato
      2                          5                 8                for one cup 

                                   x                                    for 105 cups

x = ?

jhonyy9 · Answer

5 ---- 1 cup
x ---- 105 cups
------------------

x = 105*5/1 = ?

shaleiah · Answer

525

jhonyy9 · Answer

us the rule of 3 simple

michele_laino · Answer

I write the proportion, in this way:
$$\Large  p:o:t = 2:5:8$$
so, if I apply a property of proportions, I get:
$$\Large  \left( {p + o + t} \right):o = \left( {2 + 5 + 8} \right):5$$
or this one:
$$\Large  105:o = 15:5$$
being $o+p+t=105$
please solve for $o$

anonymous · Answer

105/5=21

21 cups of onions

michele_laino · Answer

If I apply the fundamental property of proportions, I get:
$$o = \frac{{105 \times 5}}{{15}} = ...?$$

michele_laino · Answer

hint:
$$o = \frac{{105 \times 5}}{{15}} = \frac{{525}}{{15}} = ...?$$

shaleiah · Answer

35 cups

michele_laino · Answer

please wait a moment I'm checking my computation...

michele_laino · Answer

I'm very sorry, I have made a wrong reasoning

shaleiah · Answer

:(

michele_laino · Answer

please wait a moment, I'm thinking...

jhonyy9 · Answer

@Michele_Laino what is your opinion about above wrote my idea using the rule of 3 simple 

1 cup salsa 5 onion 
105 cup salsa x onion 
-------------------

x = 105*5/1 = ?

jhonyy9 · Answer

i think this is the best easy way

michele_laino · Answer

we can write this expression:
$$2N + 5N + 8N = 105$$
or:
$$15N = 105$$
where $N$ is a quantity to be determined
please solve for $N$

shaleiah · Answer

7

michele_laino · Answer

ok! So, the requested cups of onion are:
$5 \times 7=...?$

shaleiah · Answer

35

michele_laino · Answer

I don't know, since I'm not sure it is a 3 simple problem @jhonyy9 
that's right! @shaleiah

michele_laino · Answer

more precisely we have 
$2 \times 7=14$ cups of green pepper
and
$8 \times 7=56$ cups of tomato

jhonyy9 · Answer

@Michele_Laino sorry but i think now you are not right sure 

than use 2    5   8 ratio for one cup salsa 

2 cup 
5 cup   => these for one cup salsa 
8 cup 

so than for 105 cup salsa you need using 5*105 cup onion sure

michele_laino · Answer

here is my reasoning:
1 cup of salsa contains $2/ 15$ of cup of peppers, $5/15$ of cup of onions, and $8/15$ of cup of tomato
so 105 cups of salsa contains $105 \times (5/15)=35$ cups of onions

michele_laino · Answer

@jhonyy9

jhonyy9 · Answer

yes @Michele_Laino you are right sure with this reason - now i see it - this way of 3 simple not is the right way here - thank you for your help - great -

michele_laino · Answer

thanks! :) @jhonyy9