Ivan bought 3 pounds of ham and 5 pounds of cheese to make sandwiches for a picnic. He will use 1/8 pound of ham in each ham sandwich and 1/6 pound on cheese in each cheese sandwich. How many more pounds of ham will Ivan have to buy so that he can make as many ham sandwiches as cheese sandwiches?

He will need to buy 3/4 lb. more ham.

First we find out how many cheese sandwiches he can make. He uses 1/6 of a pound of cheese on each sandwich:

5:1/6 = 5/1:1/6 = 5/1*6/1 = 30

He can make 30 cheese sandwiches.

Let x be the extra ham he needs to buy:

(3+x) : (1/8) = 30

Multiply both sides by 1/8:

3+x = 30/1*1/8

3+x = 30/8 = 3 6/8 = 3 3/4

Subtract 3 from each side:

x = 3 3/4 - 3 = 3/4