Bill's Roast Beef sells 7 times as many sandwiches as Pete's Deli. The difference between their sales is 414 sandwiches. How many sandwiches did each sell?

Question

Bill's Roast Beef sells 7 times as many sandwiches as Pete's Deli. The difference between their sales is 414 sandwiches. How many sandwiches did each sell?

Answer 1

Hi, Dana.

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 = 414

So, now we can substitute for B from the equation above B = 7P

B - P = 414

7P - P = 414

6P = 414

P = 69

Therefore, Pete sells 69 sandwiches

Bill sells 7 x 69 = 483 sandwiches