Buns were being sold at three prices: One
for a penny, two for a penny and three for a
penny. Some children (there were as many
boys as girls) were given seven pennies to
spend on these buns, each child to receive
exactly the same value in buns, assuming that
all buns remained whole, how many buns
and what type did each child receive?

Question

Buns were being sold at three prices: One 
for a penny, two for a penny and three for a 
penny. Some children (there were as many 
boys as girls) were given seven pennies to 
spend on these buns, each child to receive 
exactly the same value in buns, assuming that 
all buns remained whole, how many buns 
and what type did each child receive?

mani_jha · Answer

I am working on this problem. So far I have come to this.
Let x be the no of buns bought by each child. For each child, If a1 is the no of buns of first type, a2 the buns of second type, and a3 the no of buns of third type, then the total no of buns should be:
$$a1+2a2+3a3=x$$
Now, We should find the total no of solutions of this using binomial theorem. I will post as soon as I progress more

anonymous · Answer

Did u get it?