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# Ratio and proportion AMC 8, 2010 Problem 2

## Competency in Focus:Ratio and proportion.

This problem from American Mathematics contest (AMC 8, 2010) is based on the concept of ratio and proportion and binary composition .

## Next understand the problem

[/et_pb_text][et_pb_text _builder_version="4.2.2" 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"]If $a @ b = \frac{a\times b}{a+b}$ for $a,b$ positive integers, then what is $5 @10$? $\textbf{(A)}\ \frac{3}{10} \qquad\textbf{(B)}\ 1 \qquad\textbf{(C)}\ 2 \qquad\textbf{(D)}\ \frac{10}{3} \qquad\textbf{(E)}\ 50$[/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="4.2.2" toggle_font="||||||||" body_font="Raleway||||||||" text_orientation="center" custom_margin="10px||10px"][et_pb_accordion_item title="Source of the problem" _builder_version="4.2.2" open="on"]American Mathematical Contest 2010, AMC 8  Problem 2[/et_pb_accordion_item][et_pb_accordion_item title="Key Competency" open="off" _builder_version="4.2.2"]

### Ratio and Proportion

[/et_pb_accordion_item][et_pb_accordion_item title="Difficulty Level" _builder_version="4.2.2" open="off"]2/10[/et_pb_accordion_item][et_pb_accordion_item title="Suggested Book" _builder_version="4.2.2" open="off"]

[/et_pb_text][et_pb_tabs _builder_version="4.2.2"][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="4.2.2"]Take a look at the knowledge graph first[/et_pb_tab][et_pb_tab title="HINT 2" _builder_version="4.2.2"]Substitute $a \textbf{ by } 5 \textbf{ and } b \text{ by } 10$   [/et_pb_tab][et_pb_tab title="HINT 3" _builder_version="4.2.2"]$5@10=\frac{5\times10}{5+10}=\frac{50}{15}=\frac{10}{3}$[/et_pb_tab][/et_pb_tabs][/et_pb_column][/et_pb_row][/et_pb_section][et_pb_section fb_built="1" fullwidth="on" _builder_version="4.2.2" global_module="50833"][et_pb_fullwidth_header title="AMC - AIME Program" button_one_text="Learn More" button_one_url="https://www.cheenta.com/amc-aime-usamo-math-olympiad-program/" header_image_url="https://www.cheenta.com/wp-content/uploads/2018/03/matholympiad.png" _builder_version="4.2.2" title_level="h2" background_color="#00457a" custom_button_one="on" button_one_text_color="#44580e" button_one_bg_color="#ffffff" button_one_border_color="#ffffff" button_one_border_radius="5px"]

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