34O8
Answered

Discover a world of knowledge at Westonci.ca, where experts and enthusiasts come together to answer your questions. Connect with a community of experts ready to provide precise solutions to your questions on our user-friendly Q&A platform. Discover detailed answers to your questions from a wide network of experts on our comprehensive Q&A platform.

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]

Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. Thank you for visiting Westonci.ca, your go-to source for reliable answers. Come back soon for more expert insights.