SOLUTION: Here's my problem. Please help me. Thank youuu. A machineis supposed to mix peanuts, hazelnuts, cashews, and pecans in the ratio 5:2:2:1. A can containing 500 of these mixed nut

Question 914499: Here's my problem. Please help me. Thank youuu.
A machineis supposed to mix peanuts, hazelnuts, cashews, and pecans in the ratio 5:2:2:1. A can containing 500 of these mixed nuts was found to have 269 peanuts 74 cashews and 45 pecans. How many hazelnuts are there?
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
269 peanuts, 74 cashews, and 45 pecans add up to nuts.
Since there are 500 nuts in the can,
and each nut is expected to be
either a peanut, or a hazelnut, or a cashew, or a pecan
(no almonds, chestnuts, filberts or any other nuts),
then the remaining nuts are hazelnuts.
If you want to write both calculations in one, use parentheses, like this:
,
or (showing your work)
.

Obviously, that machine is not doing a good job, or else it is mixing the bulk product correctly, but the mix segregates (de-mixes a bit) as it is being packaged.
If the nuts were in the ratio 5:2:2:1,
we could split that can containing 500 nuts into 50 groups of 10 nuts,
with each group including
5 peanuts, 2 hazelnuts, 2 cashews, and 1 pecan.

RELATED QUESTIONS
A machine is supposed to mix peanuts, hazel-nuts, cashews, and pecans in the ratio... (answered by LChester89)

A machine is supposed to mix peanuts, hazelnuts, cashews, and pecans in the ratio... (answered by parmen)

Application, I am having a hard time setting this problem up. The snack shop makes... (answered by ewatrrr)

Please help me solve this problem: A nut mix is to be prepared with cashews, almonds... (answered by checkley79,solver91311)

This is a chapter over systems and matrices.. The section is over linear equations.... (answered by richwmiller)

Can you please show me what equations to use for the following word problem: You want to (answered by josgarithmetic)

I have been struggling to figure out this problem and I was wondering if someone could... (answered by checkley77)

how do i solve this problem... Jackie wants to make a mixture of nuts to sell in her... (answered by Alan3354,scott8148,mickeysexy13)

I have posted about this problem once and it was said to not be able to be solved but it... (answered by TimothyLamb)