Bosco

At a math convention, a poll is taken about cable news.  It turns out that $5$ out of every $8$ people are bored by cable news.  If there are $120$ people at the convention, then how many people at the convention are bored by cable news?    

(5 / 8) • 120  =  75    

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When a number is reduced by 40%, the result is 36. What is the original number?    

x – (0.40 • x)  =  36    

         0.60 • x  =  36    

                   x  =  36 / 0.60    

                   x  =  60    

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What number results when 42 is increased by 120%?    

42 x 120%  =  42 x 1.20  =  35           

                      So, start with 42    

               and increase it by 35      ( "increase" means make it bigger )   

                                   total  77    

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While eating out mike and joe each tipped their server $2 mike tipped 10% of his bill and joe tipped 20% of his bill.  

What was the difference in dollars between their bills.  

Mike's Bill • 0.10 = 2    ==>>    Mike's Bill  =  2 / 0.10  =  $20    

Joe's  Bill  • 0.20 = 2    ==>>    Joe's Bill    =  2 / 0.20  =  $10    

                                    difference between their bills  =  $10    

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In a store window, there was a box of berries having a total weight of 200 kg.  The berries were 99% water, by weight.  After two days in the sun, the water content of the berries was only 90%, by weight.  What was the total weight of the berries after two days, in kg?    

You're starting with 200 kg of berries, and 99% of that is water.  

Since they're 99% water, that means that there's 1% of solid stuff.  

1% of 200 kg means that there are 2 kg of solid stuff.   

Some of the water evaporates in the sun, but the solid stuff doesn't.  

So, after the evaporation, there still remains the same 2 kg of solid stuff.  

Since the new water content is 90%, that means that now the solid stuff is 10%.  

So 2 kg (the solid stuff) is 10% of the total weight.  

That means the new total weight is 20 kg.  

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The product of a set of distinct positive integers is $630$. If one of the numbers is 42, what are the other two numbers?    

630 divided by 42 is 15.  The factors of 15 are 3 and 5.    

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There are approoximately 0.4536 kilograms in a pound. To the nearest whole pound, how many pounds does a steer that weights 200 kg weigh?  

When you aren't sure which number to multiply by which other number, think about cancelling units.   

                                  1  pound              200  kilogram        200  pound    

                           ––––––––––––––   x  ––––––––––––  =  ––––––––––  =  440.917 pounds    

                            0.4536  kilogram                1                       0.4536    

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Fill in the blanks with positive integers:    

(3 + sqrt(6))*3 = ___ + ___ * sqrt(6)    

3 • [3 + sqrt(6)]   =   9 + 3 • sqrt(6)     

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Expand (sqrt(x) + 3x)*4 + (sqrt(x) - 3x)*4.    

                4 • [sqrt(x) + 3x]   —>>>    4 sqrt(x) + 12x   

                4 • [sqrt(x) – 3x]    —>>>   4 sqrt(x) – 12x   

add them together                            8 sqrt(x)   

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