How many books did she read?

​Last year Kristen read one fourth as many biographies as mysteries and eighteen more science fiction books than biographies. The number of nature books that she read was one less than the difference between the number of mysteries and the number of biographies. If Kristen read four times as many science fiction books as nature books, than how many books did she read in all?

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x = number of biographies
4x = number of mysteries {read 1/4 as many biographies as mysteries}
x + 18 = number of science fiction books {18 more science fiction than biographies}
(x + 18)/4 = number of nature books {read 4 times as many science fiction as nature}

(x + 18)/4 = 4x - x - 1 {number of nature was 1 less than difference between mysteries and biographies}
(x + 18)/4 = 3x - 1 {combined like terms}
x + 18 = 12x - 4 {multiplied entire equation by 4 to clear fraction}
18 = 11x - 4 {subtracted x from both sides}
22 = 11x {added 4 to both sides}
x = 2 {divided both sides by 11}

x = 2 biographies
4x = 8 mysteries
x + 18 = 20 science fiction
(x + 18)/4 = 5 nature

Total
= 2 + 8 + 20 + 5
= 35 books read in all

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