Alright, to start off, this question gives us enough information for two equations. The first one is the total of Allan and Dave's scores, which is 375. If we use the letter a for Allan's score, and the letter d for Dave's score, we can make our first equation, which is a+d=375. The second equation comes from the fact that we know that Allan's score was 60 points less than double the score of Dave's. This means that a=2d-60.
Now, we'll start with the first equation, a+d=375. Because we also know that a=2d-60, we can substitute 2d-60 into the first equation for a, which changes the equation into (2d-60)+d=375
IN this new equation, our first step is to get rid of the parenthesis. Because they aren't really important in this equation, we can just get rid of them without doing anything, changing the equation from (2d-60)+d=375 into 2d-60+d=375. N
Next, we can simplify that equation by adding the numbers with the same variables, changing the equation from 2d-60+d=375 into 3d-60=375.
Now, we want to try and get d alone. To do this, we need to add 60 to both sides of the equation, changing it from 3d-60=375 to 3d=435.
Finally, we just need to divide both sides by 3 to get d all alone, changing the equation from 3d=435 to d=145, which means that Dave's score is 145!
Next, we need to plug the score we just found back into one of the original equations. It looks like it will be easier to substitute d=145 into the first equation, a+d=375. This changes the equation to a+145=375, and our final step is to subtract 145 from both sides, leaving us with a=230, which is the other half of our answer. Now we know that Dave's score was 145 and Allan's score was 230!
What you're seeing here is 12 being multiplied by its reciprocal. 12 * 1/12 = 1. This is an example of a multiplicative inverse; a multiplicative inverse is when you multiply a number by its reciprocal (1 over the number).
