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?
To solve these problems, we can use algebraic equations and solve for the unknown values. Let's go through each question step by step.
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 assume the original price of each pen is 'x' cents.
- Mr. Badger bought 12 pens every month, so the total cost for each month would be 12x cents.
- When the price rose to 15 cents, he can now only buy 10 pens with the same total cost. So the total cost is now 10 * 15 = 150 cents.
- We can set up an equation based on this information: 12x = 150.
- Solving this equation will give us the value of 'x', which is the original price of each pen.
2. There are 41 pigs and chickens on a farm. If there are 100 legs counted altogether, how many of each animal are there?
- Let's assume the number of pigs is 'x' and the number of chickens is 'y'.
- Pigs have 4 legs, so the total number of legs contributed by pigs is 4x.
- Chickens have 2 legs, so the total number of legs contributed by chickens is 2y.
- The total number of legs counted altogether is 100, so we can set up an equation: 4x + 2y = 100.
- Additionally, we know that there are 41 animals in total: x + y = 41.
- Now we have a system of two equations, which we can solve simultaneously to find the values of 'x' and 'y'.
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 assume the total number of people on full staff is 'x'.
- On that day, 5/6 of the staff came to work, so the number of people who came to work is (5/6)x.
- If three more people had been away, the fraction would have decreased to 3/4. So the number of people who came to work would be ((5/6)x - 3).
- We can set up an equation: ((5/6)x - 3) = (3/4)x.
- Solving this equation will give us the value of 'x', which represents the number of people on full staff.
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 assume the ages of Mrs. Grant, Tess, Carly, and Troy are 'x', 'y', 'z', and 'w' respectively.
- Based on the given information, we can set up an equation for the average of their ages: (x + y + z + w)/4 = 39.
- Additionally, we know that Mrs. Grant was 20 when Tess was born, so we can set up another equation: y - x = 20.
- Carly was born 2 years later than Tess, so we have another equation: z - y = 2.
- Troy was born 4 years after Carly, so we have one more equation: w - z = 4.
- Now we have a system of four equations, which we can solve simultaneously to find the ages of Mrs. Grant and her three children.