Question

The sum of two numbers is 80. If the larger number exceeds four times the smaller by 5, what is the smaller number?
A.5
B.15
C.20
D.25

Answer 1

Hint: We can take the two numbers as two variables. Then we can equate their sum. After that we can use the given relation to find another equation. Then we can solve these equations to get the value of the smallest number.

Complete step-by-step answer:
Let x be the largest number and y be the smallest number.
It is given that sum of the numbers is 80. So, we can write,
 $x + y = 80$
We can rearrange the equation.
 $ \Rightarrow x = 80 - y$ .. (1)
Then it is given that the larger number exceeds four times the smaller by 5. So, we can write this as an equation in terms of the variables.
 $ \Rightarrow x = 4y + 5$ … (2)
On substituting equation (1) in (2), we get,
 $ \Rightarrow 80 - y = 4y + 5$
On rearranging, we get,
 $ \Rightarrow 80 - 5 = 4y + y$
On further simplification, we get,
 $ \Rightarrow 5y = 75$
On dividing throughout with 5, we get,
 $ \Rightarrow y = \dfrac{{75}}{5}$
 $ \Rightarrow y = 15$
We assumed that y is the smaller number. So, the smaller number is 15.
So, the correct answer is option B.

Note: We used the concept of mathematical modelling to form mathematical equations from the given statement. While taking the variable, we must specifically state which one is the smaller number and which is the larger number. Otherwise, we will need to find the value of both the variables and compare them to get the smallest number. We must read the given statement carefully before forming the equations.