Splitting restaurant bill

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Whenever I eat at a restaurant the bill gets handed to me as I work in finance! I've gotten myself confused with how to work out the bill, so just would like to understand this for future.

So, the bill comes to £115 (including tip) and there are 3 people. 1 person would like to pay £10 more than the other 2 people. How can I work out what each person is to pay? If you could please let me know step by step how you get to the answer, it would be greatly appreciated.

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Suppose the 2 other people wish to pay £$x$, where $x$ is just a number. Then the other person wants to pay £$x+10$.

In total, then, $x + x + (x+10) = 3x+10$ pounds is payed.

So we need $3x+10=115$. Rearrange (that is, subtract $10$ from both sides and divide by $3$) to get $x = 35$, i.e. the two people should pay £$35$, and the other person £$45$.

Indeed, you can verify that $35+35+45=115$.