The sum of two numbers is 30. the difference of twice the larger number and three times the smaller number is 5. what is the positive difference between the two numbers?

Let’s give these two numbers variables
Let ‘a’ be the larger number
Let ‘b’ be the smaller number

Now from the question we know:
a + b = 30 or a = 30 - b
2a - 3b = 5

Now, let’s plug the first equation into the second to find ‘b’:

2(30 - b) - 3b = 5
60 - 2b - 3b = 5
60 - 5b = 5
55 = 5b
b = 11

Now we solve for ‘a’:
a = 30 - b
a = 30 - 11
a = 19

Now the question asks for the positive difference between the two numbers, so:
a - b = ?
19 - 11 = 8

Hope this helps!

A’b’c’ are the coordinates to the new location of the transformed triangle abc. find the distance between the coordinates points to use for your calculations.