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------------------------------------------------ Abby has twice as many books as Bob, and Jane has three times as many books as Abby, Bob, and Jane have combined. If they have a total of 372 books, how many books does each of them have?

a) Abby: 248, Bob: 62, Jane: 62
b) Abby: 124, Bob: 62, Jane: 186
c) Abby: 124, Bob: 62, Jane: 124
d) Abby: 62, Bob: 124, Jane: 186

Question

High School

Answer :

KurtDavies KurtDavies · Answer 1 · 2025-05-20T18:14:04-04:00

Abby has 124 books, Bob has 62 books, and Jane has 186 books. This satisfies the conditions of the problem where their combined total is 372 books.

Let's define variables based on the information given:

Let B be the number of books Bob has.

Then, Abby has 2B books because she has twice as many as Bob.

Jane has three times as many books as the sum of Abby, Bob, and Jane's books combined.

Let's denote the total number of books they have as 372.

The equation can be formulated as follows:

Total books = Bob's books + Abby's books + Jane's books = 372

So, B + 2B + 3 * (B + 2B + J) = 372

Simplifying, we get:

3B + 3*(3B) = 372

3B + 9B = 372

12B = 372

Solving for B:

B = 31

Now, we calculate the number of books each person has:

So, the correct option is:

b) Abby: 124, Bob: 62, Jane: 186