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Sagot :
Answer:
160 pages
Explanation:
[tex]Day\ 1 = \frac{1}{4}[/tex]
[tex]Day\ 2 = \frac{1}{3}Remainder[/tex]
[tex]Left = 80[/tex]
Required
The number of pages
Let the number of pages be x.
So, on day 1; we have:
[tex]Day\ 1 = \frac{1}{4}x[/tex]
After day 1, there are:[tex]\frac{3}{4}x[/tex] left ----------------- i.e x - 1/4x
On day 2, we have:
[tex]Day\ 2 = \frac{1}{3} * \frac{3}{4}x[/tex]
[tex]Day\ 2 = \frac{1}{4}x[/tex]
At this point, we have:
[tex]Day\ 1 = \frac{1}{4}x[/tex]
[tex]Day\ 2 = \frac{1}{4}x[/tex]
[tex]Left = 80[/tex] ---- pages left
The summation of all must equal x, the book pages
[tex]Day\ 1 + Day\ 2 + Left = Total\\[/tex]
[tex]\frac{1}{4}x + \frac{1}{4}x+ 80= x[/tex]
Simplify the left-hand side
[tex]\frac{1}{2}x+ 80= x[/tex]
Collect like terms
[tex]x - \frac{1}{2}x= 80[/tex]
Simplify
[tex]\frac{2-1}{2}x= 80[/tex]
[tex]\frac{1}{2}x= 80[/tex]
Multiply by 2
[tex]2 * \frac{1}{2}x= 80*2[/tex]
[tex]x = 160[/tex]
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