Problem number 22. Five girls ate some plums. Lauren ate two plums more than Sophie. Betty ate three plums fewer than Lauren. Claire ate one plum more than Betty and three plums fewer than Alice. Which two girls ate the same number of plums? A. Claire and Lauren. B. Claire and Sophie. C. Lauren and Alice. D. Sophie and Alice. Or E. Alice and Betty. We don't know how many plums were eaten in total and we don't really know how many each girl ate. We do however know the differences between the numbers of plums that they ate. So for this type of problem I find it helpful to draw a number line and we're just going to make the marks. We don't have to put in actual numbers. We're going to use the clues that we have in the problem to place these girls in order on the number line. And we should end up with two of them in the same spot. The first thing we can use is that Lauren ate two plums more than Sophie. So we can place Lauren and Sophie. We'll put Lauren in the middle to start. And she ate two plums more than Sophie. So Sophie ate two less. So one, two. Sophie will go right here. The next statement talks about Betty and Lauren. Betty ate three plums fewer than Lauren. We have Lauren here and Betty ate three plums less. So one, two, three. Betty will be right here. Next we have a statement that says that Claire ate one plum more than Betty and three plums fewer than Alice. Of these three girls, Betty is already on our number line. Claire ate one plum more than Betty. And also Claire ate three plums fewer than Alice. So Alice ate three more than Claire. Claire is right here. So one, two, three. Alice will be right here. We've used all our statements and we do have two girls at the same mark on our number line. Sophie and Claire. And that's answer B. Claire and Sophie.

plum consumption

number line

girls comparison

equal amounts

Sophie and Claire