数学求值问题！！希望同胞们帮帮忙！

yvonnemo

During a sale, a clothing store sold each shirt at a price of $15 and each sweater at a price of $25.Did the store sell more sweaters than shirts during the sale?



(1)The average (arithmetic mean) of the prices of all of the shirts and sweaters that the store sold during the sale was $21.



(2)The total of the prices of all of the shirts and sweaters that the store sold during the sale was $420.

本人知道这道题怎么做但是有一疑问，希望牛人指导。。
第二个条件是15x+25y=420。有什么方法可以一眼就看出来这个公式有多个配对方式？有一些DS的题给的也是这种方式，但是只有一个值，有的有多个。一般我都要带数进去算，浪费时间。有没有牛人可以指教一下！！

yiw006

DS 不需要求出值, 只要條件符合可以求出值即可 [ask yourself whether is it enough to find the answer? ]

shirleyzhou

我看到的办法是：
15x+25y=420，化简为3x+5y=84,
因为5y是5的倍数只可能以0和5为个位数，
想要得出84的个位4，3x的个位就必须是4或者9.
然后在找0<3x<84中找个位是4或者9的3的倍数，
3x=9, 24, 54,69 就这4个了。
(这一步还是比较麻烦，不放心就只有列出来，其实不用全找出来，只要找到两个就能证明不充分了。）
此时5y分别取75,60,30,15。