There is a (common) error, or some confusion, in each of the following situations. Find the error/confusion, and explain why some thinking was off, even though the person thought the thinking was all right.
A) Before summer school, a student had completed 96 units, with a GPA of 2.9. The student takes two three-unit courses in summer school and gets an A and a B for a 3.5 GPA. The student is pleased on calculating and finding the new GPA to be 3.2.
B) A teenager says she never has anything nice to wear. Her parents tell her she can buy four new blouses for her birthday but to keep the average price at $25 (or less). The girl finds some $40 blouses she really likes and calculates from $\frac { 40 + x } { 2 }$ = 25 that x = 10. So a $40 blouse and a $10 blouse would give an average of $25. She is happy to find an acceptable $10 blouse on a sale table. She buys that one and three of the $40 blouses in different colors.
C) A person bought a used car and wants to check its gas mileage. For the first few fill-ups, she covered 823 miles and got 24.4 miles/gallon. The next fill-up, after 240 more miles, took 6 gallons, so she got 40 miles/gallon. She calculates $\frac { 24.4 + 40 } { 2 }$ = 32.2 miles/gallon.

Question

There is a (common) error, or some confusion, in each of the following situations. Find the error/confusion, and explain why some thinking was off, even though the person thought the thinking was all right.
A) Before summer school, a student had completed 96 units, with a GPA of 2.9. The student takes two three-unit courses in summer school and gets an A and a B for a 3.5 GPA. The student is pleased on calculating and finding the new GPA to be 3.2.
B) A teenager says she never has anything nice to wear. Her parents tell her she can buy four new blouses for her birthday but to keep the average price at $25 (or less). The girl finds some $40 blouses she really likes and calculates from $\frac { 40 + x } { 2 }$ = 25 that x = 10. So a $40 blouse and a $10 blouse would give an average of $25. She is happy to find an acceptable $10 blouse on a sale table. She buys that one and three of the $40 blouses in different colors. 
C) A person bought a used car and wants to check its gas mileage. For the first few fill-ups, she covered 823 miles and got 24.4 miles/gallon. The next fill-up, after 240 more miles, took 6 gallons, so she got 40 miles/gallon. She calculates $\frac { 24.4 + 40 } { 2 }$ = 32.2 miles/gallon.

Quizplus · Accepted Answer

The Answer of There is a (common) error, or some confusion, in each of the following situations. Find the error/confusion, and explain why some thinking was off, even though the person thought the thinking was all right.
A) Before summer school, a student had completed 96 units, with a GPA of 2.9. The student takes two three-unit courses in summer school and gets an A and a B for a 3.5 GPA. The student is pleased on calculating and finding the new GPA to be 3.2.
B) A teenager says she never has anything nice to wear. Her parents tell her she can buy four new blouses for her birthday but to keep the average price at $25 (or less). The girl finds some $40 blouses she really likes and calculates from $\frac { 40 + x } { 2 }$ = 25 that x = 10. So a $40 blouse and a $10 blouse would give an average of $25. She is happy to find an acceptable $10 blouse on a sale table. She buys that one and three of the $40 blouses in different colors. 
C) A person bought a used car and wants to check its gas mileage. For the first few fill-ups, she covered 823 miles and got 24.4 miles/gallon. The next fill-up, after 240 more miles, took 6 gallons, so she got 40 miles/gallon. She calculates $\frac { 24.4 + 40 } { 2 }$ = 32.2 miles/gallon.

There Is a (Common) Error, or Some Confusion, in Each 40+x2\frac { 40 + x } { 2 }240+x​

There Is a (Common) Error, or Some Confusion, in Each $\frac { 40 + x } { 2 }$