Mr. Badger bought 12 pens every month until their price rose to 15 cents each. Now he can only afford to buy 10 pens at the same total cost as before. What was the original price of each pen?

There are 41 pigs and chickens on a farm. If there are 100 legs counted altogehter, how many of each animal are there?

One day, 5/6 of the office staff came to work. If three more had been away, this fraction would have decreased to 3/4. How many people are on full staff?

Mrs. Grant was 20 when her eldest child, tess, was born. Carly was born 2 years later and Troy another 4 years later. Now the average of their four ages is 39. How old are Mrs. Grant and her three children?

Please help...

Sure, I'd be happy to help you with your questions! Let's take them one at a time.

1. To solve this problem, we can set up an equation. Let's call the original price of each pen "x". So when Mr. Badger bought 12 pens, he spent 12 times x cents. When the price rose to 15 cents each, he could only buy 10 pens for the same total cost. So, the equation would be 12x = 10 * 15. Solving this equation for x, we get x = 12 * 15 / 10 = 18 cents. Therefore, the original price of each pen was 18 cents.

2. Let's call the number of pigs "p" and the number of chickens "c". Each pig has 4 legs and each chicken has 2 legs. So the total number of legs can be expressed as 4p + 2c. Since there are 41 animals and a total of 100 legs, we can set up the equation 4p + 2c = 100 and p + c = 41. From the second equation, we can express p as 41 - c. Substituting this into the first equation, we get 4(41 - c) + 2c = 100. Simplifying this equation, we find that c = 14 and p = 41 - 14 = 27. Therefore, there are 27 pigs and 14 chickens on the farm.

3. Let's call the total number of people on full staff "x". According to the information given, 5/6 of the staff came to work, which means (5/6)x. If three more people had been away, the fraction would have decreased to 3/4, which means (3/4)(x + 3). Setting up an equation, we have (5/6)x - 3 = (3/4)(x + 3). Solving this equation, we find that x = 24. Therefore, there are 24 people on full staff.

4. Let's start by assigning variables to each person's age. Let Mrs. Grant's age be "G", Tess's age be "T", Carly's age be "C", and Troy's age be "Y". We are given that Tess is 20 years younger than Mrs. Grant, so T = G - 20. Carly was born 2 years after Tess, so C = T + 2 = G - 20 + 2 = G - 18. Troy was born 4 years after Carly, so Y = C + 4 = G - 18 + 4 = G - 14. The average of their four ages is 39, so (G + T + C + Y) / 4 = 39. Substituting the values of T, C, and Y, we get (G + (G - 20) + (G - 18) + (G - 14)) / 4 = 39. Simplifying this equation, we find that G = 46, T = 26, C = 28, and Y = 32. Therefore, Mrs. Grant is 46 years old, Tess is 26 years old, Carly is 28 years old, and Troy is 32 years old.

I hope that helps! Let me know if you have any more questions.

Sure! I can help you with all of these problems step-by-step. Let's start with the first problem.

1. Mr. Badger bought 12 pens every month until their price rose to 15 cents each. Now he can only afford to buy 10 pens at the same total cost as before. What was the original price of each pen?

Let's set up an equation to solve this problem. Let the original price of each pen be x cents.

When Mr. Badger bought 12 pens at the original price, he paid 12x cents.
When he can only afford to buy 10 pens at the new price of 15 cents each, he pays 10 * 15 = 150 cents.

Now we can set up the equation:
12x = 150

To solve for x, divide both sides of the equation by 12:
x = 150 / 12 = 12.5

Therefore, the original price of each pen was 12.5 cents.

Now let's move on to the second problem.

2. There are 41 pigs and chickens on a farm. If there are 100 legs counted altogether, how many of each animal are there?

Assuming each pig has 4 legs and each chicken has 2 legs, we can set up a system of equations to solve this problem.

Let's represent the number of pigs as p and the number of chickens as c.

From the given information, we have two equations:
p + c = 41 (equation 1)
4p + 2c = 100 (equation 2)

To solve this system of equations, we can use the substitution method.

From equation 1, we can express c in terms of p:
c = 41 - p

Substituting this expression for c in equation 2:
4p + 2(41 - p) = 100
4p + 82 - 2p = 100
2p = 18
p = 18 / 2
p = 9

Substituting the value of p back into equation 1:
9 + c = 41
c = 41 - 9
c = 32

Therefore, there are 9 pigs and 32 chickens on the farm.

Now let's move on to the third problem.

3. One day, 5/6 of the office staff came to work. If three more had been away, this fraction would have decreased to 3/4. How many people are on full staff?

Let's represent the total number of people on full staff as x.

According to the problem, 5/6 of x people came to work, which means (5/6)x people came to work.

If three more people had been away, the fraction would have decreased to 3/4, so (5/6)x - 3 = (3/4)x.

To solve this equation, we can multiply both sides by 24 to eliminate the fractions:
24[(5/6)x - 3] = 24[(3/4)x]
20x - 72 = 18x
20x - 18x = 72
2x = 72
x = 72 / 2
x = 36

Therefore, the total number of people on full staff is 36.

Now let's move on to the fourth problem.

4. Mrs. Grant was 20 when her eldest child, Tess, was born. Carly was born 2 years later, and Troy another 4 years later. Now the average of their four ages is 39. How old are Mrs. Grant and her three children?

Let's represent Mrs. Grant's age as G, Tess's age as T, Carly's age as C, and Troy's age as Y.

According to the problem, Mrs. Grant was 20 when Tess was born. So, T = 20.

Carly was born 2 years later, so C = T + 2.
Troy was born another 4 years later, so Y = T + 6.

Now, the average of their four ages is 39, so (G + T + C + Y) / 4 = 39.

Substituting the values of T, C, and Y:
(G + 20 + (20 + 2) + (20 + 6)) / 4 = 39
(G + 20 + 22 + 26) / 4 = 39
(G + 68) / 4 = 39

To solve for G, multiply both sides by 4:
G + 68 = 156
G = 156 - 68
G = 88

So, Mrs. Grant is 88 years old.

Substituting the value of G into the expressions for T, C, and Y:
T = 20
C = 20 + 2 = 22
Y = 20 + 6 = 26

Therefore, Mrs. Grant is 88 years old, Tess is 20 years old, Carly is 22 years old, and Troy is 26 years old.

I hope this helps! Let me know if you have any further questions.

To find the original price of each pen, we can set up an equation based on the given information.

Let's assume the original price of each pen was x cents.

Mr. Badger bought 12 pens every month, so the total cost was 12x cents per month.
But when the price rose to 15 cents each, his budget only allows him to buy 10 pens for the same total cost.
Therefore, the total cost of buying 10 pens at 15 cents each is 10 * 15 = 150 cents.

Setting up the equation:
12x = 150

To solve for x, we can divide both sides of the equation by 12:
x = 150 / 12
x = 12.5

Therefore, the original price of each pen was 12.5 cents.

To solve the second problem:

Let's assume the number of pigs is p and the number of chickens is c.

The total number of pigs and chickens is given as 41:
p + c = 41 ---(1)

The total number of legs counted together is given as 100.
Since each pig has 4 legs and each chicken has 2 legs:
4p + 2c = 100

To simplify this equation, we can divide both sides by 2:
2p + c = 50 ---(2)

Now we have a system of linear equations (Equations 1 and 2) that we can solve to find the values of p and c.

By solving the system of equations, we find that there are 28 pigs and 13 chickens on the farm.

For the third problem:

Let's assume the full staff size is represented by x.

According to the given information, 5/6 of the staff came to work on a particular day. Therefore, the number of people who came to work is (5/6)x.

If three more people had been away, the fraction of people who came to work would have decreased to 3/4. This can be written as:

(5/6)x - 3 = (3/4)x

To solve for x, we can cross-multiply and solve the resulting equation:
4 * (5/6)x - 4 * 3 = 3x
20x/6 - 12 = 3x
20x - 72 = 18x
2x = 72
x = 36

Therefore, there are 36 people on full staff.

Finally, for the fourth problem:

Let's assume the age of Mrs. Grant is G, the age of Tess is T, the age of Carly is C, and the age of Troy is R.

According to the given information, Mrs. Grant was 20 when Tess was born. This means that the age difference between them is T - G = 20.

Carly was born 2 years after Tess, so the age difference between Carly and Tess is C - T = 2.

Troy was born 4 years after Carly, so the age difference between Troy and Carly is R - C = 4.

The average of their four ages is 39:
(G + T + C + R) / 4 = 39

We can substitute the age differences into this equation and solve for the ages:

(G + G + 20 + 2 + G + 20 + 2 + G + 20 + 4) / 4 = 39
(4G + 68) / 4 = 39
4G + 68 = 156
4G = 156 - 68
4G = 88
G = 88 / 4
G = 22

Using the age differences, we can find the ages of the children:
T = G + 20 = 22 + 20 = 42
C = T + 2 = 42 + 2 = 44
R = C + 4 = 44 + 4 = 48

Therefore, Mrs. Grant is 22 years old, and her three children are 42, 44, and 48 years old.

1.

new price x cents
solve 10x = 12(15)

2. number of chickens --- x
number of pigs --- 41-x

solve : 2x + 4(41-x) = 100

3. number of people --- x
(5/6)x - 3 (3/4)x

4. let the number of year since Troy was born be x
Mrs. Grant = 20+6+x
Tess = 6+x
Carly = 4+x
Troy = x

solve : 26+x + 6+x + 4+x + x = 4(39)