Yes, but it's actually much simpler

If you compare the two,

One is buying 4 popcorn and 3 nachos, and having $3.50 left.

The other has 3 popcorn and 4 nachos, and having $4.50 left.

Notice that for both, they have 3 popcorn and 3 nachos in common.

The difference is 1 popcorn and 1 nacho.

Now difference in spending is $1 for the cases, since $4.50 - $3.50 = $1


This tells you that 1 popcorn combo cost $1 more than 1 nacho combo.


So if a nacho combo costs $6, then a popcorn combo costs $7 since it's $1 more.


Total amount of money
= 3 x $6 + 4 x $7 + $3.50
= $18 + $28 + $3.50
= $49.50

(Based on 3 nachos 4 popcorn)

Or

4 x $6 + 3 x $7 + $4.50
= $24 + $21 + $4.50
= $49.50

(Based on 4 nachos 3 popcorn)