If a student wishes to have a ratio of 2:7 red pens to yellow pens in their pencil case: a) if they have 50 pens total what is the maximum amount they can carry with them b) if they have 18 red and 31 yellow what is the maximum amount they can carry

a) 50 pens total. 2 + 7 = 9. Number of pens is done in 9s.  50/9 = 5r5, so multiple of 5.  Then 25 + 75 pens.    10 red and 35 yellow, 45 pens             
b) 18 red / 2 = [9]r0   31 yellow / 7 = [4]r3    So could have 9 sets of reds and 4 sets of yellows but as needs to be an exact ratio we have to pick the lower number, so 24 + 74 pens.     8 red and 28, 36 pens.