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?
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)
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
I really liked that question :)
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)
Gee Chris, and I thought I was the expert in turning mole hills into mountains LOL