Help with system of equations: using profits

[notgoodatmath]

I've been having a difficult time with system of equations I was wondering if I could have some assistants with system of equations. Here's the question

Question: Keller industries' profits were up $ 20,000 this year over last year. This was an increase of 25%.

a. Let T represent the profit this year and L the profit from last year and write a system of equations that can be used to determine the profits.b. Which method would be most efficient to solve this system (addition method or substitution method)? Explain

c.Using your system to determine the profit for this year and last year.

Two pieces of information are given:
∙ This year's profit is $20000 more than last year's profit.
∙ The increase is 25%.
You should write both in equation form. Then you get a system of two equations with two variables, which you can solve.

But how do i write the equations?
I have a few thoughts.

 

[SuperSonic4]

I've been having a difficult time with system of equations I was wondering if I could have some assistants with system of equations. Here's the question

Question: Keller industries' profits were up $ 20,000 this year over last year. This was an increase of 25%.

a. Let T represent the profit this year and L the profit from last year and write a system of equations that can be used to determine the profits.b. Which method would be most efficient to solve this system (addition method or substitution method)? Explain

c.Using your system to determine the profit for this year and last year.

Two pieces of information are given:
∙ This year's profit is $20000 more than last year's profit.
∙ The increase is 25%.
You should write both in equation form. Then you get a system of two equations with two variables, which you can solve.

But how do i write the equations?
I have a few thoughts.

What thoughts have you had? Do you know how to express percentage increases?

 

[notgoodatmath]

What thoughts have you had? Do you know how to express percentage increases?

Not exactly because I'm not sure were exactly to start. I know theirs two equations on for one year with a 200,000 increase than last year which was 25% more. But I don't understand where to start the problem? Is their two equations?

 

[SuperSonic4]

Not exactly because I'm not sure were exactly to start. I know theirs two equations on for one year with a 200,000 increase than last year which was 25% more. But I don't understand where to start the problem? Is their two equations?

There will be two equations - Part A pretty much tells you it's needed: One will be the absolute increase (20,000) and the other will be the percentage increase (25%)

For the first equation: This year's profit (T) is going to be last year's profit (L) + any extra (20,000).

For the second equation: T will be L multiplied by 1+%change/100 (25%)

 

[CellCoree]

First, congratulations on taking on the challenge of solving a system of equations! It can definitely be a tricky concept to grasp, but with some practice and guidance, I'm sure you'll get the hang of it.

To start, let's define our variables. As given in the question, let T represent the profit this year and L represent the profit from last year. Now, let's think about what we know about these profits.

We are told that this year's profit (T) is $20,000 more than last year's profit (L). This can be written as the equation T = L + 20,000. This equation represents the increase of $20,000.

We are also told that the increase is 25%. This means that this year's profit (T) is 25% more than last year's profit (L). In other words, T is equal to 125% of L. This can be written as the equation T = 1.25L.

Now, we have two equations with two variables (T and L) that represent the information given in the question. These equations can be used to solve for the values of T and L, which will give us the profits for this year and last year.

As for which method (addition or substitution) would be most efficient to solve this system, it really depends on your personal preference and comfort level with each method. Both methods will give you the same solution, so I would suggest trying both and seeing which one you feel more comfortable with.

To use the addition method, you would add the two equations together to eliminate one of the variables. In this case, you would add T = L + 20,000 and T = 1.25L to get 2T = 2.25L + 20,000. Then, you can solve for one of the variables and substitute that value back into one of the original equations to solve for the other variable.

To use the substitution method, you would solve one of the equations for one of the variables (let's say T = 1.25L) and then substitute that value into the other equation. This would give you one equation with one variable, which you can then solve for and use to find the value of the other variable.

I hope this helps and good luck with your problem! Remember, practice makes perfect when it comes to solving systems of equations. Keep at it and don't be afraid to