Bosco

If I give my brother 5 dollars, then we will have the same amount of money. If instead he gives me 25 dollars, then I'll have twice as much money as he will have. How much money does my brother currently have (in dollars)?    

Call M the amount currently held by Me   

Call B the amount currently held by Brother   

                                                             (M – 5)  =  (B + 5)               (eq 1)   

                                                             (M + 25)  =  2 • (B – 25)      (eq 2)   

Multiply (2) out                                        M + 25  =  2B – 50   

Multiply both sides of (1) by 2               2M – 10  =  2B + 10    

Subtract                                                –M + 35  =       – 60   

Combine like terms                               –M           =       –95     

Multiply both sides by –1                                  M  =  95   

Plug value of M into (1)                             95 – 5  =  B + 5  

Combine like terms                                          85  =  B    

My Brother currently has 85 dollars   

check answer  

Plug 95 and 85 into (2)                            (95 + 25)  =  (2)(85 – 25)   

                                                                         120  =  2 • 60   

                                                                         120  =  120  

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In Linguistics 101, the ratio of the number of juniors to the number of seniors is 3:2.  When six more juniors join the class, and one senior drops the class, the ratio of the number of juniors to the number of seniors becomes 2:3.  How many students are in the class after these changes?   

I can tell you immediately that increasing the number     

of juniors will not invert the ratio.  But I'll go through    

the motions for you anyway.     

                                                       J          3   

                                                      ––   =   ––  

                                                       S          2     

                                                   J + 6          2   

                                                   ––––   =   –––   

                                                   S – 1          3        

Cross multiply both                            2J  =  3S            (eq 1)  

                                                  3J + 18  =  2S – 2      (eq 2)      

Get either J or S in terms of the   

other.  It doesn't matter which,   

but J would be simpler.                       J  =  3S/2      

Substitute this in eq 2                (3) • (3S/2) + 18  =  2S – 2    

                                                        9S/2 + 18  =  2S – 2     

Multiply both sides by 2                      9S + 36  =  4S – 4    

Subtract 4S from both sides               5S + 36  =  –4   

Subtract 36 from both sides                    5S  =  –40     

You cannot have a negative number of seniors    

so something is wrong somewhere.  The error     

is in the initial proposition.  This problem has ...... no solution.    

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@SoulKingBrook  < destroys the concept of a triangle >      

LOL, I was afraid I'd get my hand slapped for

taking liberties with the concept of infinity. 

But wait.  Using the proposition that in infinity,   

not only are all things possible, but all things   

are inevitable. 

Just as parallel lines drawn northward on the   

earth's surface do converge at the north pole,   

might not the parallel lines in the example of   

this problem converge at infinity?  And thus   

preserving the trianglature?    

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Of the balloons recently sold by a party store, 2 were blue and 10 were other colors. Considering this data, how many of the next 18 balloons sold would you expect in be blue   

Assuming a consistent proportion, x is to 18 as 2 is to 10    

                                                         x          2     

                                                       –––  =  –––     

                                                        18        10                

cross multiply                                  10x  =  36              

                                                           x  =  3.6      

You can't have point six of a balloon,   

so round this to a whole number, one   

way or the other.  Convention would    

be to round up.     

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    >>>>>>  123 isn't a valid number in base 3  <<<<<<   

So you concluded that the intent was 122₃ + 1₃ which is 200.  Excellent.      

_.

Calculate this pls     

Nope. 

The problem has two "open" parentheses but no "closed" parentheses.   

This would have no significant effect on an addition problem, unless it    

was a result of not getting your finger off the shift key quick enough    

and typing a ( instead of the 9 that was actually intended.    

_.

WHAT IS COS 90  

The cosine is the adjacent over the hypotenuse.  

90^o would make the hypotenuse be pointing straight up.   

Call its length "infinite" although infinity is not a number.   

                                           finite number    

Anyway cos(90) would be   ––––––––––   =   ZERO   

                                                infinite  

I've broken every rule in the book against using   

infinity as a number, but I did it only to illustrate   

how to visualize a trigonometric function as the       

ratio of two sides of a right triangle.  

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If I give my brother 5 dollars, then we will have the same amount of money. If instead he gives me 25 dollars, then I'll have twice as much money as he will have. How much money does my brother currently have (in dollars)?    

Call M the original amount held by Me   

Call B the original amount held by Brother   

                                                             (M – 5)  =  (B + 5)               (eq 1)   

                                                             (M + 25)  =  2 • (B – 25)      (eq 2)   

Multiply (2) out                                        M + 25  =  2B – 50   

Multiply both sides of (1) by 2               2M – 10  =  2B + 10    

Subtract                                                –M + 35  =       – 60   

Combine like terms                               –M           =       –95     

Multiply both sides by –1                                 M  =  95   

Plug value of M into (1)                             95 – 5  =  B + 5  

Combine like terms                                         85  =  B    

My Brother currently has 85 dollars   

check answer  

Plug 95 and 85 into (2)                            (95 + 25)  =  (2)(85 – 25)   

                                                                         120  =  2 • 60   

                                                                         120  =  120  

_.

        >>>  The answer is definitely 188  <<<

        If you interpret the problem as asking for the combined total of    

        all the miles each traveler walked, then the answer is definitely    

        not 188 because 8 • 26 = 208, not 188.   

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>>>>>  so Catherine will roll 2 twos and 4 fives  <<<<<   

            instead of 2 twos, there could be 1 one and 1 four.  

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