Practical application of multiple rates, help?

I'm brand new here, and so forgive me if I placed this in the wrong section...I have no idea what to call what it is I'm looking for help on (the title was a guess). Here's my problem.

I've got a score in a game, in this example 42747. I've also got a number representing how many wins I've got (17790). However, there are two different rates of awarding game score. One rate is 1 point per win, the other rate is 6 points per win. The total points (42747) has some of both, but obviously is not made up of entirely one rate of award.

Is there an equation that can help determine how many of each rate of reward has been given to achieve the total 42747 points, where 17790 is the total number of times an award was given?

...I'm sure there must be, but it's been a decade since I took a math class. What's this type of problem called? Thanks for your help!