If the ratio of the incomes of Avand B is 3:5 and B's income is $800 more than A's what is A's income?

(A) $600

(n) $800

(C) $1000

(D) $1200

Let the incomes of A and B be represented as $ 3x $ and $ 5x $ respectively, based on the given ratio of their incomes, which is 3:5. 

According to the problem, B's income is $800 more than A's income. Therefore, we can set up the equation:

\[
5x = 3x + 800
\]

Now, let's solve this equation step-by-step:

\[
5x - 3x = 800
\]

\[
2x = 800
\]

\[
x = 400
\]

Since A's income is $ 3x $, we substitute $ x = 400 $:

\[
A's \, income = 3 \times 400 = 1200
\]

So, A's income is:

\[
\boxed{1200}
\]

**Correct Answer: (D) $1200**

Would you like further details or have any questions? Here are some related questions to expand on this problem:

1. If B's income was $1000 more than A's, what would A's income be?
2. How would the solution change if the ratio was 4:7 instead of 3:5?
3. What if A's income is $2000? How much more is B earning than A?
4. Can the same approach be used if A's income is given in percentages of B's?
5. How would the problem change if A's income was $800 more than B's?

**Tip:** Understanding ratios helps in breaking down comparative problems into simpler algebraic forms for easy solutions!

Learn how to solve a ratio and income problem involving A and B's incomes. Use algebraic equations to determine A's income when given the ratio of incomes and the difference in amounts. 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