The sum of two numbers is 30. If we double the larger number, and subtract three times the smaller number, the result is 5. What is the positive difference between the two numbers?
This link may help you a bit.
sorry! i just wrote out all my work but it randomly got deleted. the answer is 8. here's how i got it:
first, i formulated two equations using the world problem:
x + y = 30
2x = 3y = 5.
then, i isolated the variables and used subsitution, then algebra, to find the value of y (which was 11, but it doesn't matter which you find first). then i found out x (which is 19). then, i found the positive difference. so the equation would be 19 - 11 = 8.
First, let's start by creating a system of linear equations to solve. We know that both numbers added together equal 30, so we can write the equation x+y=30. [x and y represent our two numbers]
Now, for our second equation, we look at the second sentence of the problem. If x is doubled and we subtract (3y) we get 5. This can be written as 2x-3y=5.
To solve this equation, we will use substitution. We can move x to the other side of the equals sign in the first equation to get y= -x + 30.
This can be substituted into the second equasion as 2x - 3(-x+30)=5.
If simplified, this leads to 5x-90=5. If we bring 90 to the other side of the equals sign by adding 90 to both sides, we get 5x=95 or x=19.
Since x= 19, 30-19 = y. This means that y=11. The difference between 19 and 11 is 8.