Question

What is the sum of two numbers whose difference is 45, and the quotient of the greater number when divided by the lesser number is 4?
(a). 100
(b). 90
(c). 80
(d). 75

Answer 1

Hint: Find the equation involving two numbers when their difference is 45 and the quotient of the greater number when divided by the smaller number is 4. Solve the equations to find the two numbers. Add the two numbers to find the sum of the two numbers.

Complete step by step solution:

Let the two numbers be x and y.
We need two equations to solve for two unknowns. The two equations can be obtained from the given fact of difference of two numbers and the quotient of the bigger number when divided by the smaller number.
Let x be greater than y.
The difference between the two numbers is given as 45. Hence, we have:
\[x - y = 45.............(1)\]
The quotient of the bigger number when divided by the smaller number is given as 4. Hence, we have:
\[\dfrac{x}{y} = 4\]
Taking y to the other side of the equation, we have:
\[x = 4y............(2)\]
Substituting equation (2) in equation (1), we get:
$\Rightarrow$ \[4y - y = 45\]
Solving for y, we get:
$\Rightarrow$ \[3y = 45\]
$\Rightarrow$ \[y = \dfrac{{45}}{3}\]
$\Rightarrow$ \[y = 15...........(3)\]
Substituting equation (3) in equation (2), we get:
$\Rightarrow$ \[x = 4(15)\]
$\Rightarrow$ \[x = 60\]
The two numbers are 15 and 60.
The sum of the two numbers is given as:
$\Rightarrow$ \[x + y = 15 + 60\]
$\Rightarrow$ \[x + y = 75\]
Hence, the correct answer is option (d).

Note: We require at least two equations to solve the equations with two unknowns. When choosing the difference to be 45, always subtract a smaller number from the bigger number because the difference is positive.