Suppose they were all the same

Nurul bought thirty pens and erasers altogether. Each pen cost one dollar and twenty cents and each eraser cost eighty cents. She spent twenty eight dollars in all. How many pens did she buy? Try it first. Pause if you like. There are two kinds of item, with different prices. She bought thirty items altogether. Keep that number the same. Suppose all thirty items are erasers. This gives us a starting point. The value of thirty erasers is thirty times eighty cents. That is twenty four dollars. She really spent twenty eight dollars. Find the money still to be spent: twenty eight minus twenty four. Four dollars. Change one eraser into a pen. There are still thirty items. One item has changed kind. A pen costs more. One dollar and twenty cents minus eighty cents. Each swap adds forty cents. There are four dollars still to be spent. Each swap accounts for forty cents of that difference. Divide four dollars by forty cents to find the number of pens. Ten. Nurul bought ten pens. Ten swaps change ten of the thirty items into pens. Suppose they are all one kind. Find the difference from the real total. Then divide by what one swap adds.