Question

the sum of two numbers is 150. the double of the first number and 5 times of the second numbers are equal to 450.find the number?

Answer 1

Answer:

a = 100

b= 50

Step-by-step explanation:

let two numbers be a and b

Given, a + b = 150 … … … 1

2a + 5b = 450 … … … 2

From Eq.2,

2a + 5b = 450

2a + 2b + 3b = 450

2(a + b) + 3b = 450

2(150) + 3b = 450 (from 1)

300 + 3b = 450

3b = 450 - 300

3b = 150

b = 50

Now, put b = 50 in Eq. 1 ,

a + b = 150

a + 50 = 150

a = 100

Therefore, a = 100 and b = 50

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Answer 2

★ Solution :-

Let the first number be x.

Let the second number be y.

So, as per the question, the first equation is

$\sf \leadsto x + y = 150 \: \: --- (i)$

We are also given that,

The first number is doubled and then the second number had became 5 times itself.

So, as per the question, the second equation is

$\sf \leadsto 2x + 5y = 450 \: \: --- (ii)$

By first equation,

$\sf \leadsto x + y = 150$

$\sf \leadsto x = 150 - y$

Now, let's find the original value of y by second equation.

$\sf \leadsto 2x + 5y = 450$

$\sf \leadsto 2 (150 - y) + 5y = 450$

$\sf \leadsto 300 - 2y + 5y = 450$

$\sf \leadsto 300 + 3y = 450$

$\sf \leadsto 3y = 450 - 300$

$\sf \leadsto 3y = 150$

$\sf \leadsto y = \dfrac{150}{3}$

$\sf \leadsto y = 50$

Now, let's find the original value of x by first equation.

$\sf \leadsto x + y = 150$

$\sf \leadsto x + 50 = 150$

$\sf \leadsto x = 150 - 50$

$\sf \leadsto x = 100$

So, the first and second numbers are 100 and 50 respectively.