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the first day anna read a quarter of the book. on the second day she read a third of the remainder. noticed that after two days he had 80 pages left unread. how many pages did the book have?​

Sagot :

MrRoyal

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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