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1) If the expression (12-x)÷(3x) represents a non-negative integer, what is the largest possible integer value of x?

 

2) If I give my sister 17 dollars, then we will have the same amount of money. If instead she gives me 23 dollars, then I'll have three times as much money as she will have. How much money does she currently have (in dollars)?
(I got 40 for this one, why is it wrong?)

 

3) Bocephus has a bag full of nickels and dimes. If there are 3 times as many dimes as nickels, and he has $36.05 in his bag, how many nickels does he have?

Guest Aug 19, 2018
edited by Guest  Aug 19, 2018
 #1
avatar+7266 
+1

2)

 

 

Let the amount of money that I have be  a .

Let the amount of money that my sister has be  b .

 

If I give my sister 17 dollars, then we will have the same amount of money.

a - 17  =  b + 17

                               Add  17  to both sides of the equation to solve for  a .

a  =  b + 34

 

If instead she gives me 23 dollars, then I'll have three times as much money as she will have.

a + 23  =  3(b - 23)

                                         Since  a  =  b + 34 ,  we can substitute  b + 34  in for  a .

b + 34 + 23  =  3(b - 23)

                                         Simplify both sides.

b + 57  =  3b - 69

                                         Add  69  to both sides.

b + 126  =  3b

                                         Subtract  b  from both sides.

126  =  2b

                                         Divide both sides by  2 .

63  =  b

 

The sister currently has  63  dollars. And you currently have  63 + 34 dollars, which is 97 dollars. You can try to imagine actually playing out the scenarios, knowing these amounts of money to start with, to help understand. smiley

hectictar  Aug 19, 2018
edited by hectictar  Aug 19, 2018
 #2
avatar+7266 
+1

3)

 

Let the number of nickels in the bag be  n .

Let the number of dimes in the bag be  d .

 

There are 3 times as many dimes as nickels. In other words...

The number of dimes is 3 times the number of nickels.

d  =  3n

 

He has $36.05 in his bag. So he has a total of 3605 cents in his bag.

A nickel is worth 5 cents, and a dime is worth 10 cents. So...

5n + 10d  =  3605

                                    Substitute  3n  in for  d .

5n + 10(3n)  =  3605

                                    Multiply  10  and  3  to get  30 .

5n + 30n  =  3605

                                    Combine like terms.

35n  =  3605

                                    Divide both sides of the equation by  35 .

n  =  103

hectictar  Aug 19, 2018
 #3
avatar+88899 
+1

1) If the expression (12-x)÷(3x) represents a non-negative integer, what is the largest possible integer value of x?

 

(12 - x )               4           1

______  =           __   -    __     

    3x                    x           3

 

The only integer x value that will produce a positive integer here is when  x  = 3....the expression will =  1

 

 

cool cool cool

CPhill  Aug 20, 2018
edited by CPhill  Aug 20, 2018

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