matt had 10 less than 3 times as many books as nick.
Together they had 106 books. How many books did Matt have?
m = 3n - 10
3n - m = 10
n + m = 106
Add the two equations:
3n - m = 10
+(n + m = 106)
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4n = 116
n = 29
Nick had 29 books. Put that into the equation n + m = 106
29 + m = 106
m = 106 - 29
m = 77
Matt had 77 books.
Use the first equation to verify the numbers.
m = 3n - 10
77 = 3(29) - 10
77 = 87 - 10
77 = 77
Correct.