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AMC 8 USA Math Olympiad

Linear Equation AMC 8 2010 problem 21

Try this beautiful problem from AMC 8. It involves the concept that when a number is taken as a fraction. And also based upon the basic Linear Equation calculation.

[et_pb_section fb_built=”1″ _builder_version=”4.0″][et_pb_row _builder_version=”3.25″][et_pb_column type=”4_4″ _builder_version=”3.25″ custom_padding=”|||” custom_padding__hover=”|||”][et_pb_text _builder_version=”3.27.4″ text_font=”Raleway|300|||||||” text_text_color=”#ffffff” header_font=”Raleway|300|||||||” header_text_color=”#e2e2e2″ background_color=”#0c71c3″ custom_padding=”20px|20px|20px|20px” border_radii=”on|5px|5px|5px|5px” box_shadow_style=”preset3″]

What are we learning ?

[/et_pb_text][et_pb_text _builder_version=”4.1″ text_font=”Raleway||||||||” text_font_size=”20px” text_letter_spacing=”1px” text_line_height=”1.5em” background_color=”#f4f4f4″ custom_margin=”10px||10px” custom_padding=”10px|20px|10px|20px” box_shadow_style=”preset2″]Competency in Focus: Linear Equation This problem from American Mathematics contest (AMC 8, 2010 problem 21) is based on Linear Equation[/et_pb_text][et_pb_text _builder_version=”3.27.4″ text_font=”Raleway|300|||||||” text_text_color=”#ffffff” header_font=”Raleway|300|||||||” header_text_color=”#e2e2e2″ background_color=”#0c71c3″ custom_padding=”20px|20px|20px|20px” border_radii=”on|5px|5px|5px|5px” box_shadow_style=”preset3″]

First look at the knowledge graph.

[/et_pb_text][et_pb_image src=”https://www.cheenta.com/wp-content/uploads/2020/01/AMC-8-problem-21.png” align=”center” force_fullwidth=”on” _builder_version=”4.1″ custom_margin=”||||false” custom_padding=”20px||20px||false|false”][/et_pb_image][et_pb_video _builder_version=”4.1″][/et_pb_video][et_pb_text _builder_version=”3.27.4″ text_font=”Raleway|300|||||||” text_text_color=”#ffffff” header_font=”Raleway|300|||||||” header_text_color=”#e2e2e2″ background_color=”#0c71c3″ custom_padding=”20px|20px|20px|20px” border_radii=”on|5px|5px|5px|5px” box_shadow_style=”preset3″]

Next understand the problem

[/et_pb_text][et_pb_text _builder_version=”4.1″ text_font=”Raleway||||||||” text_font_size=”20px” text_letter_spacing=”1px” text_line_height=”1.5em” background_color=”#f4f4f4″ custom_margin=”10px||10px” custom_padding=”10px|20px|10px|20px” box_shadow_style=”preset2″]Hui is an avid reader. She bought a copy of the best seller Math is Beautiful. On the first day, Hui read \( \frac{1}{5}\) of the pages plus 12 more, and on the second day she read 1/4 of the remaining pages plus 15 pages. On the third day she read 1/3 of the remaining pages plus 18 pages. She then realized that there were only 62 pages left to read, which she read the next day. How many pages are in this book? (A) 120  (B) 180  (C) 240  (D) 300  (E) 240[/et_pb_text][/et_pb_column][/et_pb_row][et_pb_row _builder_version=”4.0″][et_pb_column type=”4_4″ _builder_version=”3.25″ custom_padding=”|||” custom_padding__hover=”|||”][et_pb_accordion open_toggle_text_color=”#0c71c3″ _builder_version=”4.1″ toggle_font=”||||||||” body_font=”Raleway||||||||” text_orientation=”center” custom_margin=”10px||10px”][et_pb_accordion_item title=”Source of the problem” open=”on” _builder_version=”4.1″]American Mathematical Contest 2010, AMC 8 Problem 21 [/et_pb_accordion_item][et_pb_accordion_item title=”Key Competency” _builder_version=”4.1″ open=”off”]This number theory problem is based on the concept of linear equation[/et_pb_accordion_item][et_pb_accordion_item title=”Difficulty Level” _builder_version=”4.1″ open=”off”]5/10[/et_pb_accordion_item][et_pb_accordion_item title=”Suggested Book” _builder_version=”4.1″ open=”off”]Challenges and Thrills in Pre College Mathematics Excursion Of Mathematics 

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Start with hints 

[/et_pb_text][et_pb_tabs _builder_version=”4.1″ hover_enabled=”0″][et_pb_tab title=”HINT 0″ _builder_version=”4.0.9″]Do you really need a hint? Try it first![/et_pb_tab][et_pb_tab title=”HINT 1″ _builder_version=”4.1″ hover_enabled=”0″]You can assume total number of pages to be a variable say x. [/et_pb_tab][et_pb_tab title=”HINT 2″ _builder_version=”4.1″]Every next day she is reaing a fraction of the REMAINING pages, not the total pages.[/et_pb_tab][et_pb_tab title=”HINT 3″ _builder_version=”4.1″]she also reads some more pages on each day, so we need to subtract this also to get the actual remaining page[/et_pb_tab][et_pb_tab title=”HINT 4″ _builder_version=”4.1″]At the en of third day total remining page in term of x must be 62 as state in the question.[/et_pb_tab][et_pb_tab title=”HINT 5″ _builder_version=”4.1″][/et_pb_tab][/et_pb_tabs][et_pb_text _builder_version=”3.27.4″ text_font=”Raleway|300|||||||” text_text_color=”#ffffff” header_font=”Raleway|300|||||||” header_text_color=”#e2e2e2″ background_color=”#0c71c3″ min_height=”12px” custom_margin=”50px||50px” custom_padding=”20px|20px|20px|20px” border_radii=”on|5px|5px|5px|5px” box_shadow_style=”preset3″]

Connected Program at Cheenta

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Similar Problems

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One reply on “Linear Equation AMC 8 2010 problem 21”

first day he reads x pages;
second day he reads y pages;
third day he reads z pages;
there are 62 pages are remaining;
so,Total no of pages= (x+y+z+62) pages;
According to question, x= (x+y+z+62)/5+12;
y=(y+z+62)/4+15;
z= (z+62)/3+18;
solving them,we get x=58;y=60;z=60;
So,Total no of pages in the Book=(x+y+z+62) pages= (58+60+60+62) pages=240 pages OPTION (C)

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