What does hidden question means in a math problem

Question

Kim bought sandwhiches for the football team. Each sandwhich cost $3.49. She paid $142.39, including $2.79 tax. How many sanwhiches did she buy?

Answer 1

 

Let's say purchase tax is x% and she buys n sandwiches. The cost of 1 sandwich is s, so ns is the cost of n sandwiches. To that tax has to be added: ns(1+x/100) is the actual amount paid.

Now put in some figures. ns(1+x/100)=142.39 and nsx/100=2.79, so ns+2.79=142.39, ns=139.60. the first hidden question is: does the cost of 1 sandwich (bought separately) include purchase tax? That gives us 2 scenarios:

1. $3.49 does not include tax: s=3.49 and n=139.60/3.49=40. The second hidden question is: what is the purchase tax? Answer: nsx/100=2.79; x=279/139.60=2%.
2. $3.49 does include tax: so the true cost of a sandwich is s: s(1+x/100)=3.49. But we need to know x or s to take this further. If we use x from scenario 1 then s=3.49/1.02=$3.42. And ns=$139.60, making n=139.60/3.42=40.8. So scenario 2 does not seem to apply because we had to assume x to do the calculation.

Therefore, there were 40 sandwiches and the answer to the hidden question is tax=2%.