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rehi bought 150 oranges and 100 apples for her neighbors. she divided the oranges equally among them and had 17 oranges left. she also divided the apples equally among them and had 5 apples left. how many neighbors were there?

 Jul 23, 2016

Best Answer 

 #2
avatar+128079 
+5

We need to use some logic, here

 

Let n = the number of neighbors

Let q be the number of oranges that each neighbor received

Let r be the number of apples that each received.......and we have the following system:

 

150  = q*n + 17  →    q*n  = 133      (1)

 

100  = r*n + 5 →       r*n =  95        (2)

 

Subtract (2) from (1)

 

q*n - r*n =  38     factor out n

 

n (q - r)   =  38

 

Since 38 factors as 2 * 19   or 19 * 2 ........

 

We can assume that n = 2 or n = 19

 

But...if n = 2    then  "q"  and "r"  in both (1) and (2)  would be fractions

 

So.....let us assume that n = 19

 

Then  q = 133/19 =  7

 

And r  = 95/19  = 5

 

So....there were 19 neighbors

 

Another way to do this is to factor both 133 and 95

 

133 = q * n = 7 * 19

95 =   r * n  =  5 * 19    and it would be clear that n = 19  in both (1)  and (2)

 

 

 

cool cool cool

 Jul 23, 2016
 #1
avatar+118587 
+5

rehi bought 150 oranges and 100 apples for her neighbors. she divided the oranges equally among them and had 17 oranges left. she also divided the apples equally among them and had 5 apples left. how many neighbors were there?

 

 

So the number of neigbours is a factor of 150-17 = 133

and also a factor of  100-5=95

 

now i will use the web2.0calc to tell me the factors.

 

factor(133) = 7*19

factor(95) = 5*19

 

The only common factor is 19 so there are 19 neighbours   laugh

 

 

I really liked that question :)

 Jul 23, 2016
 #2
avatar+128079 
+5
Best Answer

We need to use some logic, here

 

Let n = the number of neighbors

Let q be the number of oranges that each neighbor received

Let r be the number of apples that each received.......and we have the following system:

 

150  = q*n + 17  →    q*n  = 133      (1)

 

100  = r*n + 5 →       r*n =  95        (2)

 

Subtract (2) from (1)

 

q*n - r*n =  38     factor out n

 

n (q - r)   =  38

 

Since 38 factors as 2 * 19   or 19 * 2 ........

 

We can assume that n = 2 or n = 19

 

But...if n = 2    then  "q"  and "r"  in both (1) and (2)  would be fractions

 

So.....let us assume that n = 19

 

Then  q = 133/19 =  7

 

And r  = 95/19  = 5

 

So....there were 19 neighbors

 

Another way to do this is to factor both 133 and 95

 

133 = q * n = 7 * 19

95 =   r * n  =  5 * 19    and it would be clear that n = 19  in both (1)  and (2)

 

 

 

cool cool cool

CPhill Jul 23, 2016
 #3
avatar+118587 
0

Gee Chris, and I thought I was the expert in turning mole hills into mountains  LOL

 Jul 23, 2016
 #4
avatar
+5

Melody's solution is the only ELEGANT solution!!. Eat your heart out, CPhill!!.

 Jul 23, 2016
 #5
avatar+118587 
0

Is our guest calling my solution an elephant ??    LOL     wink

 

Thanks guest      laugh

 Jul 23, 2016
 #6
avatar+128079 
0

Eh....I'll probably get over it........

 

 

cool cool cool

 Jul 23, 2016
 #7
avatar+118587 
0

I gave you five stars Chris - you deserved them for all that effort :)

 Jul 23, 2016

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