He needs 40 buns and 40 dogs ...so he HAS to spend
40 dogs/10dogs/pkg x $ 3.50/pkg = $14 (4 packages dogs)
40 buns/8buns/pkg x $ 2.50/pkg = 12.50 (5 packages buns) 14 + 12.50 = 26.50
He has 70 - 26.50 = 43.50 left to spend
Now any combo that spends 43.50 is allowed as he has met his 40 dog-bun requirement
3.50 y + 2.50 x = 43.50
I used a graphical approach to see where x,y pairs are integer values (since you cannot split packages) you will see that
x, y = 2,11 9,6 and 16, 1 all fit the bill ....remember you have to add the obligatory red packages above !
y is dogs x is buns so 7 b 15 d 14 b 10 d and 21 b 5 d all would spend the total $70