3 years ago

Ali has 11 more than twice as many color pencils as Benji. Together they have 89 pencils.

Mathematics

1 answer:

Montano1993 [528]3 years ago

8 0

Answer:

Benji: 26

Ali:53

Step-by-step explanation:

Benji:X

Ali: 2X+11

2X+11+X=89

3X+11=89

3X=78

X=26

Benji: 26

Ali: 2×26+11=53

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$\displaystyle\bf\\Explanations:\\\\The~similarity~ratio~of~two~similar~cones=k\\\\k=is~the~ratio~between~2~corresponding~lengths\\\\k=\frac{R_1}{R_2}=\frac{h_1}{h_2}\\\\The~ratio~between~2~corresponding~areas~of~similar~cones=k^2\\\\\frac{Area~1}{Area~2}=k^2\\\\The~ratio~between~the~volumes~of~the~2~similar~cones=k^3\\\\\frac{Volume~1}{Volume~2}=k^3$

$\displaystyle\bf\\Solving:\\\\Volume1=108~m^3\\\\Volume2=4m^3\\\\k^3=\frac{108}{4}\\\\k^3=27~~\Big|\sqrt{~}\\\\k=\sqrt[\b3]{27}\\\\k=3\\\\Area1=54~m^2\\\\\frac{Area~1}{Area~2}=k^2\\\\\frac{54}{Area~2}=3^2\\\\\frac{54}{Area~2}=9\\\\Area2=\frac{54}{9}\\\\\boxed{\bf Area2=6 m^2}$