Ada and Paul received their scores on three tests. On the first test, Ada's score was 10 points higher than Paul's score. On the second test, Ada's score was 4 points higher than Paul's score. If Paul's average (arithmetic mean) score on the three tests was 3 points higher than Ada's average score on the three tests, then Paul's score on the third test was how many points higher than Ada's score?

9

14

17

23

25

##### 考题讲解

Ada 三次的分数分别是~$A_1$~,~$A_2$~,~$A_3$~ Paul 三次的分数是~$P_1$~,~$P_2$~,~$P_3$~Ada 的平均分是~$\frac{ A_1~+A_2+A_3}{3}$~ ， Paul 的平均数是 ~$\frac{P_1+P_2+P_3}{3}$~ ; Paul 的平均分比 Ada 高 3 分，所以得出~$\frac{P_1+P_2+P_3}{3}$~-~$\frac{ A_1~+A_2+A_3}{3}$~ =3，整理得出：~$P_1+P_2+P_3-(A_1+A_2+A_3)=9$~因为题目中给了两个人每次考试的分数差，因为我们可以整理成为：~$(P_1-A_1)+(P_2-A_2)+(P_3-A_3)=9$~所以，-10-4+~$(P_3-A_3)$~=9, ~$P_3-A_3$~=23