This is an interesting question. It's a min/max question disguised as a ratio question (you still need both though!) At first I did the brute force method by figuring out the ratios bought of each etc ... but took too long. So I redid the question using 2 methods: 1) Educated Guessing (about 1 min) and 2) Easier Brute Force (about 2:15). So let's get started.

1)

Educated GuessingThe idea here is to look at the product that is most bought and compare to the range of the other Deli

S1) Provolone was the largest quantity purchased at B: 7 * $18 =

$126The range at A will be

[7 * $15 =

$105, 7 * $19 =

$133]Since $126 falls between this, it might be possible for A to be greater than B

S2) American was the largest quantity purchased at A: 6 * $15 =

$90The range at B will be

[6 * $16 =

$96, 6 * $20 =

$120]Since $90 is less than $96, B will always be greater than A

2)

Easier Brute ForceThe idea here is to ignore the 6 kg and use the ratios given. The reason for this is because the 6 will complicate the calculations.

S1) The total bought is 2+7+2 = 11. So instead of buying 6kg, let's say he bought 11kg.

2*$16 + 7*$18 + 2*$20 = $32 + $126 + $40 =

$198Now the range can be calculated by using 11kg at Deli A:

[11 * $15 =

$165, 11 * $19 =

$209]Since $198 falls between this, we cannot conclude where more was spent.

S2) The total bought is 6+2+1 = 9. So instead of buying 6kg, let's say he bought 9kg.

6*$15 + 2*$17 + 1*$19 = $90+ $34 + $19 =

$143Now the range can be calculated by using 11kg at Deli A:

[9 * $16 =

$144, 9 * $20 =

$180]Since $143 is less than the minimum ($144), that means less was spent at A than B.

Let me know if there is something wrong with my logic.

Thanks,

sunz3000