Question

Mrs. Humphrey, Ms. Essner, and Mr. Verbsky can do 352 math problems per day. Mrs. Humphrey and Ms. Essner together can do 248 math problems per day, while Mrs. Humphrey and Mr. Verbsky together can do 224 math problems per day.

How many math problems can each of them do alone?
Option 1: Mrs. Humphrey: 144, Ms. Essner: 104, Mr. Verbsky: 104
Option 2: Mrs. Humphrey: 112, Ms. Essner: 136, Mr. Verbsky: 104
Option 3: Mrs. Humphrey: 104, Ms. Essner: 144, Mr. Verbsky: 104
Option 4: Mrs. Humphrey: 104, Ms. Essner: 104, Mr. Verbsky: 144

Answer 1

The problem and the given information have an error, so it is not possible to determine the number of math problems each person can do alone.

Step-by-step explanation:

Let's use algebra to solve this problem. Let's assume that Mrs. Humphrey can do x math problems per day, Ms. Essner can do y math problems per day, and Mr. Verbsky can do z math problems per day. From the given information, we have the following equations:

1. Mrs. Humphrey + Ms. Essner + Mr. Verbsky = 352
2. Mrs. Humphrey + Ms. Essner = 248
3. Mrs. Humphrey + Mr. Verbsky = 224

From equation 2, we can solve for Mrs. Humphrey in terms of y:

Mrs. Humphrey = 248 - y

Substituting this into equation 3, we get:

(248 - y) + Mr. Verbsky = 224

Simplifying, we find:

Mr. Verbsky = 224 - 248 + y

Combining the terms, we have:

Mr. Verbsky = -24 + y

Now, we can substitute these values into equation 1:

(248 - y) + y + (-24 + y) = 352

Let's simplify this equation:

248 - y + y - 24 + y = 352

248 - 24 = 352

224 = 352

This is not a true statement, so there must be an error in the problem or the given information. Therefore, it is not possible to determine how many math problems each person can do alone.