Number of footballs sold in the first half of the year (6 months) = 120 x 6 = 720
Number of footballs sold in the next 2 months = 80 x 2 = 160
Total number of footballs sold in 8 months = 720 + 160 = 880
∴ Average number of footballs sold per month (in the first 8 months) = 880 / 8 = 110

The sum of two negative integers is negative, so 'p + q' is not the answer, e.g., (−4) + (−2) = −6.
The sum of two negative integers and 1 is also negative, so 'p + q + 1' is not the answer, e.g., (−4) + (−2) + 1 = −5.
When 1 is subtracted from the sum of two negative integers, a negative number is obtained and so 'p + q − 1' is not the answer, e.g., (−4) + (−2) − 1 = −7.
Twice the sum of two negative integers is also negative, so '2(p + q)' is not the answer, e.g., 2((−4) + (−2)) = −12.
The quotient of two negative integers is always positive, so 'p / q' is the answer, e.g., (−4) / (−2) = 2.

Taking the original price of the pair of baseball gloves as $100
($100 is chosen because it is easier to convert into a percentage later),
New price after first increase = $115, i.e., 1.15 x 100
New price after second increase = $161, i.e., 1.4 x 115
∴ Increase in price = $61 and so the increase is 61%

Taking the side of the original square as x cm,
Area = (x − 7)(x + 7) = 32
x² − 49 = 32
x² = 81 or x = √81 = 9
∴ Perimeter of the original square = 4 x side = 4 x 9 cm = 36 cm

Cakes sold = (8/6) x 27 = 36; Brownies sold = (2/6) x 27 = 9; Total = 36 + 9 = 45
Alternatively, each part of the ratio = 27/6 = 4.5
Cakes and brownies together equal 10 parts (8 + 2) of the ratio.
∴ Number of cakes and brownies sold = 4.5 x 10 = 45

0.003 x 0.07 = 0.00021
Converting to percentage gives 0.00021 x 100% = 0.021%.

Sum of the parts of the ratio = 5 + 6 = 11.
Total number of students = 66; Each part of the ratio = 66 / 11 = 6.
Number of boys = 5 x 6 = 30; Number of girls = 6 x 6 = 36.
Thus, the girls outnumber the boys by 6.
Alternatively, let b and g denote the number of boys and girls, respectively.
Then, b/g = 5/6 and b + g = 66.
Eliminating b gives (5/6)g + g = 66 or (11/6)g = 66.
Thus, g = 36 and b = 30 giving g − b = 6.

There are 3600 seconds in an hour.
The factory makes 108000 buttons in one hour; so, in one second, it makes 108000 / 3600 = 30 buttons.

1 / y = 13 − (1 / 4) − (1 / 7)
1 / y = (13 x 28 − 7 − 4) / 28 = (364 − 11) / 28= 353 / 28
∴ y = 28 / 353

33 days is 2 days less than 5 weeks, since (7 x 5) − 2 = 33.
Had Ehud's homework assignment date been postponed by 35 days (5 weeks), the new submission date would have fallen on a Thursday.
Since the date was postponed by 33 days, he was supposed to now submit his homework on a Tuesday.

Number of questions solved during the second hour = 30/2.5 = 300/25 = 12.
Number of questions solved during the third hour = 30/3 = 10.
Total number of questions solved = 30 + 12 + 10 = 52.

The average (arithmetic mean) of n numbers is their sum divided by n.
The sum of all the 7 numbers is 83 x 7 = 581.
The sum of the 5 numbers is 95 x 5 = 475.
So, the sum of the other 2 numbers is (581 − 475) = 106.
Thus, the average of the other 2 numbers is (106 / 2) = 53.

Let v be the speed at which the boat is moving (relative to the ground) and u be the speed at which the stream is flowing (also relative to the ground).
When the boat travels upstream, its speed (relative to the ground) is reduced because the stream opposes the motion of the boat. So, the speed of the boat is v − u = 10.
On the other hand, when the boat travels downstream, its speed (also relative to the ground) increases and is equal to v + u = 14.
Subtracting v − u = 10 from v + u = 14 gives 2u = 4 or u = 12 miles per hour.

There are 36 possible outcomes when a pair of die are thrown as explained below.
For each number that the first dice rolls, there are 6 possible outcomes for the second dice.
For example, if the first dice rolls a 1, the second dice can roll 1, 2, 3, 4, 5 or 6.
Since the first dice can roll 6 different numbers, there are 6 x 6 = 36 different possibilities.
The only way that the numbers rolled by the two dice can sum upto 12 is if each dice rolls a 6.
Since the sum of the numbers does not equal 12 in 35 out of the total 36 possibilities, the required probability is 35 / 36.

A pack of cards typically has totally 52 cards (26 red and 26 black).
Probability = Number of favorable outcomes / Total number of possible outcomes
Number of favorable outcomes (for drawing a red card) = 26; Total number of possible outcomes = 52.
So, the required probability = 26 / 52 = 1 / 2.

Ilhan can order a pizza in 3 different ways.
For each pizza order, he has a choice of 7 drinks.
So, the total number of different orders that he can place is 3 x 7 = 21.

Rise in price = New Price − Original Price = $70 − $50 = $20.
So, percentage increase = (20/50) x 100% = 40%.

Annual interest income = $2000 x 12 = $24000.
Interest rate = Annual interest income / Amount on which interest is being earned
= (24000/400000) x 100% = 6%.

Observe that with the exception of the first 2 terms of the sequence, every term of the sequence is equal to the sum of the preceeding two terms.
So, the term appearing after 21 in the sequence is (13 + 21) = 34.
Note that this is a very well-known sequence of numbers, and is called the 'Fibonacci sequence'.

Average speed = Total distance traveled / Total time taken.
Total distance traveled = 200 + 200 = 400 miles.
Total time taken to complete both the journeys = 7 + 3 = 10 hours.
So, average speed = 400 / 10 = 40 miles per hour.

To solve such problems, consider the rate at which a person or group does a particular job.
Joshua does the job at the rate of (1/40)^th of the job per minute.
Ariel does the job at the rate of (1/60)^th of the job per minute.
When working together, their rates can be added. So, (1/40) + (1/60) = (3/120) + (2/120) = 5/120.
Joshua and Ariel together do the job at the rate of (5/120)^th of the job per minute.
Thus, time taken to complete the job working together = 120/5 = 24 minutes.

Since lamp posts are being placed at 50-foot intervals along a 1200 feet long bridge, the bridge is divided into 1200 / 50 = 24 sections.
If each section is associated with the lamp post at its end, 24 lamp posts are required.
However, one lamp post is placed at the beginning (one end) of the bridge.
So, the total number of lamp posts required is 24 + 1 = 25.
Note : In such counting problems, care must be taken to include the first and the last items that have to be counted.