9. What is the sum of two numbers whose difference is 45 and the quotient of the greater number by the lesser number is 4?

A. 100
B. 90
C. 80
D. 75



Answer :

To solve this problem, let's break it down step by step.

1. Define Variables:
- Let the lesser number be [tex]\( x \)[/tex].
- Let the greater number be [tex]\( y \)[/tex].

2. Set Up Equations from Given Conditions:
- From the problem, we know that the difference between the two numbers is 45. Therefore, we can write:
[tex]\[ y - x = 45 \][/tex]
- We are also given that the quotient of the greater number by the lesser number is 4. This gives us:
[tex]\[ \frac{y}{x} = 4 \implies y = 4x \][/tex]

3. Solve the Equations:
- Substitute [tex]\( y = 4x \)[/tex] into the first equation:
[tex]\[ 4x - x = 45 \][/tex]
- Simplify the equation:
[tex]\[ 3x = 45 \][/tex]
- Solve for [tex]\( x \)[/tex]:
[tex]\[ x = 15 \][/tex]

4. Find the Greater Number:
- Substitute [tex]\( x = 15 \)[/tex] back into the equation [tex]\( y = 4x \)[/tex]:
[tex]\[ y = 4 \times 15 = 60 \][/tex]

5. Calculate the Sum of the Two Numbers:
- Add [tex]\( x \)[/tex] and [tex]\( y \)[/tex] together:
[tex]\[ 15 + 60 = 75 \][/tex]

So, the sum of the two numbers is 75.

Therefore, the correct answer is:
(d) 75