Question

Find the numbers whose product is 150 such that the one of
the number is one more than four times the other number​

Answer 1

✬ First Number = 25 ✬

✬ Other Number = 6 ✬

Step-by-step explanation:

Given:

• Product of two numbers is 150.
• One number is 1 more than four time other number.

To Find:

• What are the two numbers ?

Solution: Let the other number be x. Therefore,

➟ First Number = 1 more than 4 times x

➟ First Number = (4x + 1)

A/q

• Product of these numbers = 150

$\implies{\rm }$ (First $\times$ Other) number = 150

$\implies{\rm }$ (4x + 1) $\times$ (x) = 150

$\implies{\rm }$ 4x² + x = 150

$\implies{\rm }$ 4x² + x – 150 = 0

Now, By using middle term splitting method

➼ 4x² + x – 150

➼ 4x² – 24x + 25x – 150

➼ 4x (x – 6) + 25 (x – 6)

➼ (x – 6) or (4x + 25)

➼ x = 6 or x = –25/6

Take the positive value of x. { Negative ignored }

So,

➯ Other number = x = 6

➯ First number = (4x + 1) = 24+1 = 25

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★ Verification ★

➛ (First Number)(Other number) = 150

➛ 25 $\times$ 6 = 150

➛ 150 = 150

[ Verified ]

Answer 2

GIVEN:

• The product of the two numbers is 150.
• One number is one more than the four times the other number.

TO FIND:

• What is the one number and another number ?

SOLUTION:

Let one number be 'x' and another number be 'y'

CASE:- ❶

➤ The product of the two numbers is 150.

According to question:-

$\bf{\dashrightarrow x \times y = 150...1)}$

CASE:- ❷ 

➤ One number is one more than the four times the other number

$\bf{\dashrightarrow x = 4y + 1...2)}$

Put the value of 'x' in equation 1)

$\rm{\dashrightarrow (4y +1)y = 150 }$

$\rm{\dashrightarrow 4y^2 + y = 150 }$

$\rm{\dashrightarrow 4y^2 + y-150 = 0 }$

$\rm{\dashrightarrow 4y ^2 +(25-24)y - 150 = 0 }$

$\rm{\dashrightarrow 4y^2 + 25y - 24y - 150 = 0 }$

$\rm{\dashrightarrow y(4y + 25) -6(4y + 25) = 0 }$

$\rm{\dashrightarrow (4y + 25) (y-6) = 0}$

$\rm{\dashrightarrow y = \dfrac{-25}{4} (Neglected)}$

$\bf{\dashrightarrow y = 6 }$

Put the value of 'y' in equation 2)

$\rm{\dashrightarrow x = 4 \times 6 + 1 }$

$\rm{\dashrightarrow x = 24 + 1 }$

$\bf{\dashrightarrow x = 25 }$

• One number = x = 25
• Another number = y = 6

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