Context: Ravi has only three types of books on his bookshelf-novels, magazines, and textbooks. All his books except X are novels, all except Y are magazines, and all except Z are textbooks. If the ratio of X : Y : Z = 35 : 22 : 27, then what is the ratio of the number of magazines to the number of textbooks on Ravi’s bookshelf?
Answer question

Let's denote the total number of books on Ravi's bookshelf as \( N \). 

Given:
- All books except \( X \) are novels, meaning there are \( N - X \) novels.
- All books except \( Y \) are magazines, meaning there are \( N - Y \) magazines.
- All books except \( Z \) are textbooks, meaning there are \( N - Z \) textbooks.

The sum of novels, magazines, and textbooks is the total number of books \( N \). Therefore:

\[
N - X + N - Y + N - Z = N
\]

Simplifying the equation:

\[
3N - (X + Y + Z) = N
\]

\[
2N = X + Y + Z
\]

\[
N = \frac{X + Y + Z}{2}
\]

The ratio given is \( X : Y : Z = 35 : 22 : 27 \).

Let's assign variables based on this ratio:
- \( X = 35k \)
- \( Y = 22k \)
- \( Z = 27k \)

Now, substitute these into the equation for \( N \):

\[
N = \frac{35k + 22k + 27k}{2} = \frac{84k}{2} = 42k
\]

Now, the number of magazines is \( N - Y = 42k - 22k = 20k \).

The number of textbooks is \( N - Z = 42k - 27k = 15k \).

The ratio of the number of magazines to the number of textbooks is:

\[
\text{Ratio of magazines to textbooks} = \frac{20k}{15k} = \frac{20}{15} = \frac{4}{3}
\]

Thus, the ratio of the number of magazines to the number of textbooks on Ravi’s bookshelf is **4:3**.

Would you like further details or have any questions?

Here are 5 related questions you might find interesting:
1. If the total number of books is 84, how many novels does Ravi have?
2. How would the ratio change if the number of novels increased by 10?
3. If the ratio of X:Y:Z were 7:5:8, what would the new ratio of magazines to textbooks be?
4. What is the total number of books if \( k = 2 \)?
5. How many textbooks are there if \( k = 3 \)?

**Tip:** When dealing with ratios, always check how they relate to the total quantities involved, especially when the sum is involved in multiple categories like in this problem.

Explore the solution to a problem involving the ratio of magazines to textbooks on Ravi's bookshelf. Understand how to calculate ratios using given data and algebraic expressions. Suitable for students in Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation