Hints and solutions to Guess and Check #3
- (a) I'm thinking of a number. If you multiply it by 3, then
subtract 5
and finally add 10, you get 20. What number am I thinking of?
- (b) I'm thinking of a number. If you multiply its square by 3 and
then
add 9, you get 117. What is that number?
- (c) I'm thinking of a number. If you subtract 4 from the number, then
multiply the result by 3 and then add 5, you get 26. What is that number?
- These are not so different from the problem about Mary and the mall -
and can be worked by the same
approaches. We'll do each of them by a different approach:
-
(a) by guess-and-check: Let's guess that the number is 3. Multiply by
3 (and get 9), then subtract 5 (and get 4) and add 10 and we get 14. Not
big enough, so try something bigger. How about 5? Multiply by 3 (and get
15), then subtract 5 (and get 10) and add 10 and get 20. So the number
was 5.
- (b) by working backwards: At the end we had 117, after adding 9. So
before we added 9 we had 108. Before that we multiplied by 3, so we
divide by 3 to get that we previously had 36. And 36 was the square of
the number we started with, so that number must have been 6 (technically,
-6 is also an answer to this problem).
- (c) by algebra: If x is the number, we have the following after all
the operations:
(x-4)*3+5 = 26 -- solving, the first step gives 3(x-4) = 21, then x-4 =
7, so x must have been 10.