<p>1-a restaurant has 19 tables that can seat a total of 84 people . some of the tables seat 4 people. and the others seat 5 people ,how many tables seat 5 people ??
(A)4
(B)5
(C)6
(D)7
(E)8
i solve it but it took alot of time ,is there any fast way to solve it ?</p>
<p>Suppose all the tables seated 4: 19 x 4 would be seating for 76.</p>
<p>But you know there’s seating for 8 more than that, and you know that all the tables that are not tables for 4 are tables for 5. That is, you know that the tables with an extra chair have only one extra chair. There have to be 8 extra chairs, so there must be 8 tables for 5.</p>
<p>Takes a lot longer to type that than it does to think it.</p>
<p>Or, you could start in the middle and try plugging in numbers.</p>
<p>Six tables for 5 means there will be 13 tables for 4.<br>
6 x 5 + 13 x 4 = 30 + 52 = 82. Not enough; need 2 more chairs, so try 8.</p>
<p>Eight tables for 5 means there will be 11 tables for 4.
8 x 5 + 11 x 4 = 40 + 44 = 84. That’s it.</p>
<p>Treat this as a two equation word problem. It’s relatively simple.</p>
<p>Let m be the numbers of tables that seat 4 and n the numbers of tables that seat 5.</p>
<p>Then:
(equation 1) 4m + 5n = 84</p>
<p>and</p>
<p>(equation 2) m + n = 19</p>
<p>From equation 2: m = 19 - n.</p>
<p>Substitute for m in equation 1: 4(19 - n) + 5n = 84 and so (carrying out the multiplication and combining terms) n = 8.</p>
<p>When I solved the problem this way it took me about 30 seconds.</p>
<p>Right, that too. I assumed that was the approach that had taken Mandour so long, but I realize that may have been a faulty assumption.</p>