首先是要用字母代替各个不同的组合。

令 only vaccinated against rubella的人数为 r

令 only vaccinated against mump的人数为 m

令 vaccinated rubella（这里面包括了only rubella和 both rubella & mump两组人数，回忆venn diagram） 为 R

令 vaccinated mump （同上，包括了 only mump 和both rubella & mump两组人数） 为M。

剩下的事情就是把题目中给的文字条件用公式表达出来：

he number of children who have been vaccinated against rubella is twice the number who have been vaccinated against mumps ：（式子 一） R= 2M （注意这里不是only rebella和only mump）。

The number who have been vaccinated against both is twice the number who have been vaccinated only against mumps ： 刚才说了R和M里面都包括了both r&m 这个子集，所以当把only rebella 和 only mump 从 R和 M内分别减去后剩下的就是 both r & m了，表达为： （式子二）R-r=M-m =2m

If 5,000 have been vaccinated against both： 跟着上面的那个式子，2m = 5000 得出 m =2500，同时得出M=3m=7500

how many have been vaccinated only against rubella？就是要求r， 把式子一代入到式子二中， R=2M=7500*2=15000.

R- r =2m =5000， 将R=15000代入，得出r =15000-5000=10000