MathDB

p1. Johnny has

5

apples. His mother gives him

8

oranges. Johnny eats

5

of these oranges, and then gives his sister, Corrine,

2

of his apples. How many pieces of fruit does he have left?
p2. Haysonne has a number of quarters, dimes, nickels, and pennies, which total to

\$2.05

. If his dimes were quarters and his quarters dimes, and his nickels were pennies and his pennies nickels, his total would be

\$2.23

. He has two more nickels than dimes and one more penny than quarters. How many nickels does Haysonne have?
p3. Angela is thinking of a perfect square. Her number contains three distinct digits, and when the tens and ones digits are flipped, the resulting number is a greater perfect square. What perfect square is Angela thinking of?
p4. Luis is a glue manufacturer. He can make one whole block of glue in five hours by himself. Marco can manufacture the same amount in three hours. How long would it take them to manufacture five blocks of glue working together at their same usual rates? Express your answer as a mixed fraction.
p5. How many triangles are in the following diagram? https://cdn.artofproblemsolving.com/attachments/1/5/c70aa0ff02afd3fce89222fd3c2c7906055002.jpg
p6. In rectangle

ABCD

, the length of

AD

8

and the length of

AB

20

. Angles ADE and BEC are congruent, and angles

DEF

and

FEC

are congruent. What is the length of

DF

multiplied by the length of

FC

? Express your answer as a common fraction. https://cdn.artofproblemsolving.com/attachments/6/1/a509ffaa599870b4fd82cf44ca8d5f9e4bf12e.png
p7. On Monday, John receives

100

dollars from his father. Over the next week, everyday there is a

50\%

chance he will receive a gift of

10

dollars from a magical Shamu. What is the probability that at the end of the week, John will have exactly

130

dollars?
p8. John creates a grid that has

2

columns and

3

rows. He wants to place the numbers

1

through

6

in this grid, with the numbers strictly increasing downwards and to the left. How many distinct grids could he create?
p9. The four vertices of a rectangle are also the vertices of a regular hexagon of side length

3

. What is the area of the rectangle? Express your answer in simplest radical form.
p10. In Amy’s area, phone numbers can have

6

digits with each digit ranging from

0

9

. Bill can only remember

5

of the

6

digits of Amy’s phone number. Bill doesn’t remember which digit he forgot nor its position in her phone number, but he remembers the order of the digits he does recall. How many different phone numbers would Bill have to dial in order to ensure that he dials Amy‘s number?
PS. You should use hide for answers. Collected [url=https://artofproblemsolving.com/community/c5h2760506p24143309]here.

Problem Statement