Okay, so let's call B = the number of sandwiches Bill sells
and P = the number of sandwiches Pete sells
Since Bill sells 7 times as many sandwiches as Pete, then
B = 7P
And the difference between their sales is 414 sandwiches. Since we know that Bill sells more than Pete, then
B - P = 434
So, now we can substitute for B from the equation above B = 7P
x = bill's
y = pete's
x = 8y
B - P = 434
7P - P = 434
6P = 434
P = 72.33
Therefore, Pete sells 72.33 sandwiches
Bill sells 7 x 72.33 = 506 sandwiches.
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