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
