Solve the following

Question

1. A well is 20 feet deep. A snail at the bottom climbs vertically up 4 feet each day and slips back 2 feet each night. How many days will it take the snail to reach the top of the well?

2. Sheena picked a basket of guavas. She gave half of the guavas to her neighbor, 8 guavas to her mother and half of the remaining guavas to her bestfriend.she kept 3 guavas for herself. How many guavas did she have at the beginning?

3. There were 61 athletes at the annual sports fest who plays for either the basketball team and 18 were in the baseball team,how many players were both in teams

4 the sum of 10 consecutive counting numbers is 155.if the least number is taken away, the average becomes 16.if 6 is added to the remaining 9 numbers.what is the new average?

5. Tom has just enough money to buy exactly 11 apples and 3 mangoes or exactly 2 apples and 5 mangoes. Danny wants only one type of fruit and has enough money to buy 1 mango but not enough for 2, or enough money to buy x apples. Find the greatest possible value of x.

Answer 1

Q1: it will take the snail 10 days to reach the top of the well.

Q2: Sheena had 44 guavas to being with.

Q3: The number of athletes is B-43.

Q4: The first number would be 11.

Q5: Danny can buy 2 apples.

Answer 2

Question No.1:

To solve this problem, we can set up an equation to represent the snail's progress:

Let's denote:

D = the depth of the well (20 feet)

U = the distance the snail climbs during the day (4 feet)

D = the distance the snail slips back during the night (2 feet)

N = the number of days it takes for the snail to reach the top

The snail climbs 4 feet each day and slips back 2 feet each night. So, during each 24-hour cycle (day and night), the snail makes a net progress of (4 - 2) = 2 feet.

We want to find out how many 2-foot cycles are needed to cover the depth of the well, which is 20 feet.

So, the equation becomes:

2 feet per day-night cycle * N cycles = 20 feet (depth of the well)

Now, let's solve for N:

2N = 20

Divide both sides by 2:

N = 20 / 2

N = 10

So, it will take the snail 10 day-night cycles, or 10 days, to reach the top of the well.

Q2. Answer

Let's denote the initial number of guavas Sheena had as "G."

Here are the steps of what Sheena did:

1. She gave half of the guavas to her neighbor, which means she gave away (1/2) * G guavas.
2. She then gave 8 guavas to her mother.
3. After that, she gave half of the remaining guavas to her best friend, which means she gave away (1/2) * (G - (1/2) * G - 8) guavas.
4. Finally, she kept 3 guavas for herself.

Now, let's set up an equation to represent these actions:

G - (1/2) * G - 8 - (1/2) * (G - (1/2) * G - 8) - 3 = 0

Let's simplify this equation step by step:

1. G - (1/2) * G is equal to (1/2) * G.
2. (1/2) * (G - (1/2) * G - 8) can be simplified as (1/2) * (1/2) * G, which is (1/4) * G.

Now, the equation becomes:

G - (1/2) * G - 8 - (1/4) * G - 3 = 0

Now, combine like terms:

(1/2) * G - (1/4) * G = (1/4) * G

Now the equation becomes:

(1/4) * G - 8 - 3 = 0

Combine the constants:

(1/4) * G - 11 = 0

Now, add 11 to both sides of the equation to isolate (1/4) * G:

(1/4) * G = 11

Now, multiply both sides by 4 to solve for G:

G = 11 * 4 G = 44

So, Sheena had 44 guavas at the beginning.

Q3. Answer

To find out how many athletes played for both the basketball and baseball teams, we can use the principle of inclusion-exclusion.

Let:

1. B represent the number of athletes on the basketball team.
2. T represent the total number of athletes at the sports fest.
3. A represent the number of athletes on the baseball team.

From the given information, we know that there were 61 athletes at the sports fest who played either basketball or baseball:

T = 61

We also know that 18 athletes were on the baseball team:

A = 18

Now, we want to find out how many athletes played both basketball and baseball, which we can represent as the intersection of B and A:

Number of athletes in both teams = B ∩ A

We can use the principle of inclusion-exclusion to find this value:

T = (Number of athletes in basketball) + (Number of athletes in baseball) - (Number of athletes in both teams)

Since we know the values of T, A, and the number of athletes in baseball, we can rearrange this equation to solve for the number of athletes in both teams:

Number of athletes in both teams = (Number of athletes in basketball) + (Number of athletes in baseball) - T

Number of athletes in both teams = B + A - T

Substituting the values we have:

Number of athletes in both teams = B + 18 - 61

Number of athletes in both teams = B + 18 - 61 Number of athletes in both teams = B - 43

So, the number of athletes who played for both the basketball and baseball teams is B - 43.

Q4. Answer

Let's solve this step by step:

1.   The sum of 10 consecutive counting numbers is 155.

Let the first number in the sequence be "x." Since they are consecutive counting numbers, the next nine numbers will be x+1, x+2, x+3, ..., x+9.

The sum of these numbers is given as 155:

x + (x+1) + (x+2) + (x+3) + (x+4) + (x+5) + (x+6) + (x+7) + (x+8) + (x+9) = 155

Now, we can simplify this equation:

10x + 45 = 155

Subtract 45 from both sides:

10x = 155 - 45 10x = 110

Now, divide by 10:

x = 11

So, the first number is 11, and the sequence is 11, 12, 13, …, 19, 20.

1. If the least number is taken away, the average becomes 16.

If we take away the number 11 from the sequence, we are left with the numbers 12, 13, 14, 15, 16, 17, 18, 19, and 20. The average of these numbers is given as 16:

(12 + 13 + 14 + 15 + 16 + 17 + 18 + 19 + 20) / 9 = 16

Now, let's find the sum of these remaining numbers:

(12 + 13 + 14 + 15 + 16 + 17 + 18 + 19 + 20) = 144

1. If 6 is added to the remaining 9 numbers, what is the new average?

Adding 6 to each of the remaining 9 numbers:

(12 + 6) + (13 + 6) + (14 + 6) + (15 + 6) + (16 + 6) + (17 + 6) + (18 + 6) + (19 + 6) + (20 + 6) = 150 + 9(6) = 150 + 54 = 204

Now, we have the new sum of the numbers. To find the new average, divide this sum by 9 (since there are 9 numbers):

New average = 204 / 9 = 22.67 (rounded to two decimal places)

So, the new average of the numbers, after adding 6 to each of the remaining 9 numbers, is approximately 22.67.

Q5. Answer

Let's break down the given information step by step:

1. Om's options:
2. Om can buy either 11 apples and 3 mangoes or 2 apples and 5 mangoes.
3. Danny's options:
4. Danny wants either only mangoes or only apples.
5. He can buy 1 mango but not 2.
6. He can buy x apples.

Now, let's analyze these options:

1. Since Danny can buy 1 mango but not 2, the cost of 1 mango must be less than or equal to the cost of 2 apples.
2. Let's assume the cost of 1 mango is "M" and the cost of 1 apple is "A."
3. From the given options, we know that Om can buy either 11 apples and 3 mangoes or 2 apples and 5 mangoes. So, we can create two equations based on these options:

Equation 1: 11A + 3M Equation 2: 2A + 5M

Now, we want to find the greatest possible value of x (the number of apples Danny can buy). Since Danny can buy only 1 mango, let's set M = 1:

Equation 1 becomes: 11A + 3(1) = 11A + 3 Equation 2 becomes: 2A + 5(1) = 2A + 5

Now, we need to compare the cost of 1 mango (which is 1) to the cost of 2 apples. To do that, set the two equations equal to each other:

11A + 3 = 2A + 5

Now, subtract 2A from both sides of the equation:

9A + 3 = 5

Subtract 3 from both sides:

9A = 2

Now, divide by 9:

A = 2/9

So, the cost of 1 apple is 2/9 of the cost of 1 mango.

Now, let's find out how many apples Danny can buy:

Since Danny can buy only 1 mango, he must have enough money to buy 2 apples (because the cost of 2 apples is equivalent to the cost of 1 mango).

Therefore, the greatest possible value of x is 2. Danny can buy 2 apples.