Question 1189249
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There are some great answers already. I'll post a different viewpoint.


L = number of pencils in one large bag
s = number of pencils in one small bag


3s = number of pencils from the three small bags only
19L = number of pencils from the 19 large bags only
19L+3s = number of pencils total from all bags mentioned
19L+3s = 224
This is one of the equations in the system.


The goal is to find the number k such that L+s = k
We're given five possible answer choices: {16,36,42,19,18}. The value k takes on one of those numbers.


If k = 16, then we have this system
{{{system(L+s = 16,19L+3s = 224)}}}
Solving that system leads to (L,s) = (11,5)
So this is one possible solution.


If k = 36, then we have this system
{{{system(L+s = 36,19L+3s = 224)}}}
Solving that system leads to (L,s) = (7.25,28.75)
We can rule this out because L and s must be positive whole numbers.


If k = 42, then we have this system
{{{system(L+s = 42,19L+3s = 224)}}}
Solving that system leads to (L,s) = (6.13,35.88)
This can be ruled out for similar reasoning as above.


If k = 19, then we have this system
{{{system(L+s = 19,19L+3s = 224)}}}
Solving that system leads to (L,s) = (10.44,8.56)
This can be ruled out for similar reasoning as above.


If k = 18, then we have this system
{{{system(L+s = 18,19L+3s = 224)}}}
Solving that system leads to (L,s) = (10.63,7.38)
This can be ruled out for similar reasoning as above.


In short, choices B through E can be ruled out because they lead to L & S being nonwhole decimal numbers. Only choice A is valid.


I skipped the steps in solving each system, so let me know if you need to see those steps. 
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