## College Algebra (6th Edition)

Let $L$ represent the amount of times the word "love" was uttered, $S$ represent the amount of times the word "sorry" was uttered and $T$ the amount of times the word "thanks" was uttered. The exercise tells us the following: $$L = S + 419$$ $$T = S + 32$$ $$L + T + S = 1,084$$ This is a system of three variables, which can be solved by substituting the values of L and T into the last equation: $$(S + 419) + (S + 32) + S = 1,084$$ $$3S + 451 = 1,084$$ $$3S = 633$$ $$S = 211$$ Knowing $S$, we can find $L$: $$L = (211 + 419) = 630$$ and $T$: $$(211 + 32) = 243$$