1. The sum of the ages of Ed and his father is 59 years. If his father's age is 11 years less than four times Ed's age, how old is Ed?

2. Five less than seven times a certain number is 58.Find the number.

3. The sum of 1/2 a certain number and 1/3 of the same number is 30. Find the number.

#1.

First, we represent the unknown using variables.
Let x = Ed's age
Let 59 - x = father's age (since according to the first statement, the sum of their ages is 59)
Then we setup the equation. According to the second statement,
Father's age = 4*(Ed's age) - 11
In variables,
59 - x = 4x - 11
59 + 11 = 4x + x
70 = 5x
(5x)/5 = (70)/5
x = 14 years old [Ed's age]

#2.
Represent the unknown with a variable.
Let x = number
Then setup the equation using the given conditions.
7x - 5 = 58
Solving for x,
7x = 58 + 5
7x = 63
x = 9

#3.
Represent the unknown with a variable.
Let x = number
Setup the equation:
(1/2)x + (1/3)x = 30
Solve for x. (Recall how to add fractions too)
(3/6)x + (2/6)x = 30
[(5/6)x]*(6/5) = 30*6/5
x = 36

Hope this helps~ :)

4. The perimeter of a tgriangle is 44 inches. If one side is 5 inches longer than the smallest side and the largest side is 1 inch less than twice the smallest side, how many inches are there in the smallest side?

#4.

Represent the unknowns with a variable.

Let x = smallest side
Let x + 5 = larger side (according to the 2nd statement)
Let 2x - 1 = largest side (according to the 2nd statement)
Then setup the equation. Recall that the perimeter of a triangle is just the sum of the lengths of its sides:
x + x + 5 + 2x - 1 = 44

Now solve for x. Units in inches.

Hope this helps~ :)

thank you for help

I have two more question, I hope you can help me.

1. A hotel has 120 rooms. If the number of double room is 8 more than three times the number of single rooms, how many single rooms does the hotel have?

2. A mechanic earns $5 more per hour than his helper. On a six-hour job the two men earn a total of $114. how much does each earn per hour?

1. Let's solve this problem step by step.

- Let's assume Ed's age is "x" years.
- According to the given information, Ed's father's age is 11 years less than four times Ed's age. So, his father's age can be represented as 4x - 11.
- The sum of Ed's age and his father's age is 59, so we can write the equation as:
x + (4x - 11) = 59.
- Simplifying the equation: 5x - 11 = 59.
- Adding 11 to both sides of the equation: 5x = 70.
- Finally, dividing both sides by 5: x = 14.
- Therefore, Ed is 14 years old.

2. Let's solve this equation:
- Let's assume the certain number is "x".
- According to the given information, five less than seven times the certain number is equal to 58. We can write the equation as:
7x - 5 = 58.
- Adding 5 to both sides of the equation: 7x = 63.
- Finally, dividing both sides by 7: x = 9.
- Therefore, the certain number is 9.

3. Let's solve this equation:
- Let's assume the certain number is "x".
- According to the given information, the sum of 1/2 of the certain number and 1/3 of the same number is 30. We can write the equation as:
(1/2)x + (1/3)x = 30.
- To combine fractions, we need a common denominator, which in this case is 6. So, the equation becomes:
(3/6)x + (2/6)x = 30.
- Simplifying the equation: (5/6)x = 30.
- Multiplying both sides by the reciprocal of 5/6 (which is 6/5):
x = (30 * 6/5).
- Solving the equation: x = 36.
- Therefore, the certain number is 36.