They actually spent $25 + $2 tip = 27 and got back $1 each which = 30. In the first equation, the tip is part of the $27 dollars, but then calculated again instead of the $3 they got as change.

280

If you read and analyze it more, we solved the Math differently and wrong. It is like saying -1 - (-1) = 0.

9 times.

33

A + 2A - 4B + 7B + 2C - 5C = 16 + 83
3A + 3B - 3C = 99 => 3(A + B - C) = 99
=> A + B - C = 99/ 3 =>
A + B - C = 33

Fill up the 3 gallon container first. Pour it into the five gallon container. Fill up the 3 gallon container again, and fill up the rest of the 5 gallon container, and you should have 1 gallon left over in the 3 gallon container.

43 is the largest number that cannot be made using the numbers 6, 9, and 20.

Every natural number is member of one of the following six series:

0, 6, 12, 18, ...
1, 7, 13, 19, ...
2, 8, 14, 20, ...
3, 9, 15, 21, ...
4, 10, 16, 22, ...
5, 11, 17, 23, ...
If for a number in one of these series holds that it can be made using the numbers 6, 9, and 20, then this also holds for all subsequent numbers in the series (by adding a multiple of 6).

To find out what the largest number is that cannot be made using the numbers 6, 9, and 20, we therefore only need to know, for every series, what the smallest number is that can be made in that way.

In the series 0, 6, 12, 18, ... the smallest number that can be made is 0, so there is no number that cannot be made.
In the series 1, 7, 13, 19, ... the smallest number that can be made is 49 (20+20+9), so 43 is the largest number that cannot be made.
In the series 2, 8, 14, 20, ... the smallest number that can be made is 20, so 14 is the largest number that cannot be made.
In the series 3, 9, 15, 21, ... the smallest number that can be made is 9, so 3 is the largest number that cannot be made.
In the series 4, 10, 16, 22, ... the smallest number that can be made is 40 (20+20), so 34 is the largest number that cannot be made.
In the series 5, 11, 17, 23, ... the smallest number that can be made is 29 (20+9), so 23 is the largest number that cannot be made.

Nine days.

4 crayons.

1.5

5 / 36

1. Calculate the probability of guessing the first number correctly. Since there are 6 possible numbers, the probability is 1/6
2. Calculate the probability of guessing the second number incorrectly. Since Todd has already guessed the first number correctly, there are 5 remaining numbers to choose from, so the probability is 5 / 6
3. Since these are two independent events, multiply their probabilities to find the overall probability:
(1/6) * (5/6) = 5/36

888 + 88 + 8 + 8 + 8 = 1000