Are the equations for these questions right?

1) Erik has 2 part-time summer jobs. For Job 1 he gets $9/hr on weekdays and for Job 2 he gets $12/hr for weekends. Last week he worked 23 hours and he earned a total of $231. How many hours did he work on the weekend?
9x+12y = 231
x + y = 23

2) Find two numbers such that four times the larger increased by 1/4 of the smaller is 42 and the difference between 3 times the larger and 1/2 the smaller is 26.
4x+y = 42
3+y = 26

3) The perimeter of a public swimming pool is 112m. If 5 times the length equals 12 times the width. Find the dimensions of the pool.
5x+12y = 112
x+y = 112

4) The sum of Bruce's age and his younger brother Lou's age is 110 years. Ten years ago the difference in their ages was 10 years. How old are they now?
x + y = 110
x-y = 10

The first is correct.

2. Should be 4x + (y/4) = 42
3x - (y/2) = 26

3 and 4 are also incorrect.
For #3, they tell us that 5 times the length eauals 12 times the width.
that translates to 5x = 12y. Can you get the second equation? (remember the perimeter is 2 x length + 2 x width.
Then see fi you can correct #4.

is the 2nd equation 2x + 2y = 112

I don't get 4...
I'm sure the 1st equation is x+y = 110 but I can't figure out the 2nd.

yes, that is right..2x + 2y = 112.

And, yes the first equation for #4 is
x + y = 110. For the second equation...remember, it is 10 years ago...we have to take 10 off each of their ages...(x-10) - (y-10) = 10.

Do you understand?

9

Yes thanks so much!

you're welcome!

Let's go through each equation and check if they are set up correctly.

1) Erik's two jobs are categorized as Job 1 and Job 2. The given information states that he earns $9 per hour for Job 1 and $12 per hour for Job 2. Last week he worked a total of 23 hours and earned $231. We need to determine how many hours he worked on the weekend.

To set up the equations, we can assign variables:
Let x represent the number of hours Erik worked on weekdays (Job 1).
Let y represent the number of hours Erik worked on weekends (Job 2).

The equation representing the total earnings is correct:
9x + 12y = 231

However, the equation representing the total number of hours worked is not correct. To find the solution, we need to set up an equation representing the total hours worked:
x + y = 23

Therefore, the correct set of equations is:
9x + 12y = 231
x + y = 23

2) We need to find two numbers such that four times the larger increased by 1/4 of the smaller is 42, and the difference between 3 times the larger and 1/2 the smaller is 26.

Let x represent the larger number.
Let y represent the smaller number.

The equation representing the first condition is correct:
4x + (1/4)y = 42

However, the equation representing the second condition is incorrect. The difference between two expressions should be represented by subtraction, not addition:
3x - (1/2)y = 26

Therefore, the corrected set of equations is:
4x + (1/4)y = 42
3x - (1/2)y = 26

3) The problem involves finding the dimensions of a swimming pool based on the given information.

Let x represent the length of the pool.
Let y represent the width of the pool.

The equation representing the perimeter of the pool is incorrect. The correct equation should be the sum of all four sides of the pool, rather than just two sides:
2(x + y) = 112 (since perimeter = 2 length + 2 width)

The equation representing the ratio between the length and width is correct:
5x = 12y

Therefore, the corrected set of equations is:
2(x + y) = 112
5x = 12y

4) The problem involves finding the ages of Bruce and Lou based on the given information.

Let x represent Bruce's age.
Let y represent Lou's age.

The equation representing the sum of their ages is correct:
x + y = 110

The equation representing the difference in their ages ten years ago is incorrect. The correct equation should be subtraction, not addition:
x - y = 10

Therefore, the corrected set of equations is:
x + y = 110
x - y = 10