Last week, Ellen bought 4 apples for $2.40. This week she bought 9 apples for $5.40. If the cost per apple remains the same, how many apples could she buy next week?

1 apples for 1.20
6 apples for 3.40
10 apples for 6.00
13 apples for 8.20

If Ellen bought 4 apples for $2.40, then the cost per apple is 2.40/4 = $<<2.4/4=0.60>>0.60.

If the cost per apple remains the same, she could buy 10 apples for 6.00 next week. Answer: \boxed{10}.