Answer:
a) 56 shells in each jar
b) 297 shells were picked
c) 2, 8, 14, 20, ... shells were discovered (=2+6n); 47, 48, 49, 50, ... shells in each jar (=47+n); for n=0, 1, 2, 3, ...
Step-by-step explanation:
a)
The first digit is given as 5. The second is 9 less than 3 times 5, so is
3×5 -9 = 15 -9 = 6
The 2-digit number that is Sally's house address is 56.
Sally originally planned to put 56 shells in each jar.
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b)
If each of the 5 jars has 56 shells, and Sally collected 17 more than that, she originally picked ...
5×56 +17 = 280 +17 = 297
Sally originally picked 297 shells.
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c)
We saw that the number of shells to go into jars is 280. That will fill 6 jars with ...
280/6 = 46 4/6 . . . . shells in each jar
That is, Sally can fill 6 jars with 46 shells each, and have 4 shells left over. The number of additional shells to put the same number in each jar will be a number that makes a multiple of 6 when 4 is added to it. Already we know that adding 2 shells will bring the total to 6 "extra", so will allow 1 more shell to be added to each of the 6 jars.
additional shells = 2 +6n . . . . . . for some whole number n
number in each jar = 47 +n . . . . . for the same whole number n
Sally could have discovered, 2, 8, 14, ... shells in her pocket.
