The difference between two numbers is 45. Three times the larger number less five times the smaller number equals 75. What are the two numbers?
nvm. i figured it out :)
how to do it pls
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To find the two numbers, let's assign variables to them. Let's call the larger number 'x' and the smaller number 'y'.
According to the problem, the difference between the two numbers is 45. So, we can set up the first equation as:
x - y = 45 ---(1)
The second piece of information states that three times the larger number minus five times the smaller number equals 75:
3x - 5y = 75 ---(2)
Now, we have a system of two equations (equation 1 and equation 2) with two variables (x and y). To solve this system, we can use a method called substitution or elimination.
Let's use the elimination method. We can multiply equation (1) by 3 and equation (2) by 1 to make the coefficients of 'x' in both equations the same:
(3)(x - y) = (3)(45)
3x - 3y = 135 ---(3)
(1)(3x - 5y) = (1)(75)
3x - 5y = 75 ---(4)
Now, subtract equation (3) from equation (4):
(3x - 5y) - (3x - 3y) = 75 - 135
3x - 5y - 3x + 3y = -60
-2y = -60
y = (-60) / (-2)
y = 30
Now that we have the value of 'y' as 30, we can substitute it back into equation (1) or (2) to find the value of 'x'.
Using equation (1):
x - y = 45
x - 30 = 45
x = 45 + 30
x = 75
Therefore, the two numbers are x = 75 and y = 30.