Question 1192480
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Let x be the number of candies each of the 16 students got.  Then the total number of candies is 16x.<br>
Each of 7 students gave up 3/5 of their share, which was divided equally among the other 9 students, giving each of those other students 14 more candies.<br>
{{{(7*(3/5)x)/9=14}}}
{{{(21/5)x=126}}}
{{{x=126(5/21)=6*5=30}}}<br>
ANSWER: The number of candies in the bag was 16x = 16*30 = 480<br>
Solving the problem using formal algebra was a good exercise, but somewhat awkward.<br>
Solving the problem informally is better for teaching problem-solving skills -- and it provides good exercise in logical reasoning.<br>
9 students got an additional 14 candies each; that's 9*14=126 candies.
Those 126 candies were the contributions of 7 students; the contribution from each of those 7 students was 126/7=18.
The 18 candies each of those 7 students gave up was 3/5 of their original allotment; their original allotment was 18(5/3)=30.
The 16 students originally got equal numbers of candies, so the number of candies in the bag was 30*16=480.<br>