Chloe scored 41 points in seven basketball games. If she keeps scoring at this rate, about how many points will she score in the next four games? (A) 10 points, (B) 24 points, (C) 35 points, (D) 41 points, or (E) 70 points.
Let’s think for a minute. We know that Chloe scored 41 points in seven games. We’re trying to think if this pattern continues, how many points she would score in the next four games? So we think seven divided by two is 3.5, and 3.5 is almost four. And that means we can estimate how many points she might score in four games by also dividing 41 by two. 40 divided by two is 20, and one divided by two is a half. 41 divided by two is 20.5. We would expect that she would score a little more than 20.5, and, of course, we know that she can’t score half a point. Looking at our answer choices, it seems like the closest option would be 24. This is a great way to use rates to do some estimation.
Now if we wanted to take a mathematical approach, we can go back to our ratio and say 41 points over seven games will be equal to 𝑃, the number of points she would score in four games. And to solve for 𝑃, we would cross multiply. 41 times four must be equal to seven times 𝑃. 41 times four equals 164, and that equals seven times 𝑃. To find what 𝑃 is equal to, we need to divide both sides by seven. To do this division, seven goes into 16 two times with the remainder of two. Seven goes into 24 three times with the remainder of three. We can write this as the mixed number 23 and three-sevenths. If 𝑃 is equal to 23 and three-sevenths, using this method, we see that we would expect Chloe to score just over 23 points, which confirms our estimate of 24 points, option (B).
If Chloe continues at this rate, we can expect her to score about 24 points in the next four games.