19. Sarah is on a diet. She can only eat 1/4 lb. of turkey breast for lunch. She stops by the deli and orders 1/4 lb of turkey breast. The clerk slices off 3 slices (all the same size) and weighs them. The three slices weigh a total of 1/3 lb. Sarah says, "I can't eat 1/3 lb. I'm on a diet." The clerk says, "Fine, I'll only charge you for 1/4 lb. Sarah says, "But I can't eat 1/3 lb. I'm on a diet." The clerk says, then just eat "1/4 lb. and give the rest to your dog." How many slices can Sarah eat?

If we want to use the A = RB technique, we would need to find the number of slices per pound. We would then multiply that times the number of pounds which Sarah can eat, 1/4, to find the number of slices. If 3 slices weigh 1/3 lb the rate is

We need to divide 3 by 1/3 to get the rate

If there are 9 slices in a pound, there will be 1/4 of that in 1/4 lb, and 9 x 1/4 = 9/4 slices. We may want to express that as a mixed number.

This problem can also be done using ratio and proportion. Set up the following table.

This gives rise to the following equation

When we multiply both sides by 1/4 we get

which is the same answer we got the other way. She should eat 2 and 1/4 slices of turkey breast if she wants to limit hser consumption of turkey breast to only 1/4 lb.