Answer:
Horatio spends 30 hours on the more difficult book and 10 hours on the lighter book
Step-by-step explanation:
Let X be the hours spent reading the more difficult book
Let Y be the hours spent reading the less difficult book
Total hours spent = X + Y = 40
Number of pages of difficult book in X hours at 12 pages per hour = 12X
Number of pages of easier book in Y hours at 25 pages per hour = 25Y
Total pages read = 12X + 25Y
So we have two equations in X and Y and we can solve them simultaneously. Equations are:
X + Y = 40 (1)
12X + 25Y = 610 (2)
We can eliminate one of the variable terms by making the coefficients of the other term equal and then subtracting
Multiply (1) by 12 to make X terms equal
12(X + Y) = 12 x 40
12X + 12Y = 480 (3)
Subtract (3) from (2)
(2) - (3)
==> 12X + 25Y - (12X + 12Y) = 610 - 480
==> 12X + 25Y - 12X - 12Y = 130
==> 25Y - 12Y = 130 (12X terms cancel)
==> 13Y = 130
==> Y = 130/13 (divide both sides by 13)
==> Y = 10
Using (1)
X + Y = 40
==> X + 10 = 40
==> X + 10 - 10 = 40 - 10
==> X = 30
So answer:
Horatio spends 30 hours on the more difficult book and 10 hours on the lighter book
