Marcus collects donations and sends care packages to troops overseas. He has 36 bars of soap and 24 toothbrushes and wants to arrange the items so the packages are identical. What is the greatest number of packages that Marcus can make using all the soap and toothbrushes? What is the greatest number of packages of soap and toothbrushes that Marcus can make? 》 Marcus can make at most? 12 packages How many bars of soap and toothbrushes are in each package? 0 There are bars of soap and ? toothbrushes in each package.

Answer:Marcus can make 12 packages, with 2 toothbrushes and 3 bars of soap in each package.Step-by-step explanation:For all the packages to be identical, they must all contain the same numbers of soaps and the same nuber of toothbrushes.The ratior of soaps to brushes is 36/24 = 3/2He could make 24 packages, each with 1 tootbrush and (3/2) bars of soap.Assuming he is not going to cut soap bars in half, that is no good.To make the numbers of individual items come out as integers, the smallest number he can multiply them by is the denominator on the (3/2) bar of soap. That would be a 2.So he can makes packages with toothbrushes =    2 x 1 =2                                                 and soap bars    = 3/2 x 2 = 3He can put 5 items in each package - 3 soap bars and 2 toothbrushes.That means he makes 12 packages.