# Hard math question?

1. Find the smallest integer which, when divided by each of the integers 2 through 10, gives in each case a remainder that is 1 less than the divisor

2. Prizes cost 15, decorations 25, and cake 10. The cake wasn't taxed, but the other items were taxed for a total tax of 2.8. What was the tax rate?

3.You have \$100 to buy 100 books. You can pay in \$10, \$3, and \$.5 How many each type do you buy?

4. Write 16 using six 5's and any operation

5. Find the 200th digit of 1/13th

6. Find a number which, when decreased by 23, one-fourth the result is as much less than 37 as the number is greater than 56. What is the number?

Relevance

1. Not sure I understand the question. Do you mean the smallest integer such that when divided by any integer 2-10 always gives a remainder of 1? If so, find the least common multiple 2520 and then add 1 = 2521. If you divide this number by any number between 2 and 10 inclusive, you will get a remainder of 1.

2. 15+25 = 40

40*x=2.8

x=0.07, 7% tax rate

3. Let x = # of \$10 books, y = # of \$3 books, and z = # \$0.50 books. x, y and z are all elements of the set of natural numbers.

x + y + z = 100

10x + 3y + 0.5z = 100

therefore 19x +5y =100

since x, y, and z all must be natural numbers, the only pair x and y that solve this equation are x = 5, y = 1 therefore buy 5 \$10 books, 1 \$3 book and 94 \$0.50 books

4. 5*5-5-5+(5/5) = 16

5. 1/13 is a repeating decimal .076923 repeating.

200 mod 6 = 2, so its the second digit = 7.

6. 209