- It can be done with three. You might think two at first. After all, if you find that one basket has two more than the other, you know the total number of apples. And if they are the same, you also know. But if one has 1 more, you don’t. You have two possibilities, and must count a third basket.
- One. Let the number of sunny side up eggs eaten be x. We know that 12-3.5x equals 5. If we subtract 12 from both sides, we see that -3.5x equals -7. Finally, divide both sides by -3.5 to see that x=2. 2 sunny side up eggs were eaten, and therefore one remains.
- You drew 10 triangles. If you drew all triangles, you would have had only 3*15=45 sides. You need 5 more. You have to draw 5 squares to increase 45 to 50. This means that 15-5 = 10 of the shapes were triangles.
- 18. Let the number of oranges in a small bag be x, and that in large bags, y. 8x=5y+14, and x+5=y. Substitute y to get 8x=5x+25+14. Subtract 5x from both sides to see that 3x equals 39. Divide both sides by 3 and find that there are 13 oranges in a large bag. 13+5 = 18 oranges in a large bag.
- 21! The largest number that cannot be made in groups of a and b is ab-a-b, where a and b are relatively prime. If a is 10 more than b, then a(a-10)-a-a+10=199, and so a2-12a+10=199, so a2-12a-189=0. (a-21)(a+9)=0, and so a is either 21 or -9. Only 21 is positive, so it is the solution.
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