Question

the sum of two numbers is 150.the double of the first number and five time of the second number make 450. find the numbers.

Answer 1

Answer:

sum of two numbers is 150

Let the number be 10x + y

so 10X + Y = 150 ..........eq 1

Now

Double the first number = 2(10x)

Five times second number = 5(y)

20X + 5y = 450 ......eq 2

Now Subtract.eq 1 and 2

( 10X. + Y = 150) * 3

20x + 5y = 450

Multiply eq 1 with 2

20x + 2y = 300

- 20x - 5y = 450

- 3y = - 150

y = 150/3 = 50

Now subsititute y value in eq 1

10X + 50 = 150

10x = 150-50

x = 100/10 => 10

Y = 50 X = 10

verification :- 10(10) + 50 = 150

Answer 2

The two numbers are 100 and 50

Given : The sum of two numbers is 150. The double of the first number and five time of the second number make 450.

To find : The numbers.

Solution :

We can simply solve this mathematical problem by using the following mathematical process. (our goal is to determine the two numbers)

Let, the first number = x

and, the second number = y

According to the data mentioned in the question,

x + y = 150 ...(1)

And,

(2 × x) + (5 × y) = 450

2x + 5y = 450 ...(2)

Now, multiplying the equation (1) with 2 :

2 × (x+y) = 2 × 150

2x + 2y = 300 ...(3)

Now, subtracting equation (3) from equation (2) :

‎ ‎ ‎ ‎ 2x + 5y = 450

(-)‎ 2x + 2y = 300

‎ ‎ ‎ - ‎ ‎ ‎ ‎ ‎-‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎‎ ‎ ‎-

____________________

‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎5y-2y = 450-300

‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ 3y = 150

‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ y = 150/3

‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ y = 50

Now, substituting the value of y in equation (1)

x + 50 = 150

x = 150 - 50

x = 100

So, the first number = x = 100

The second number = y = 50

(These will be considered as the final result.)

Hence, the two numbers are 100 and 50

#SPJ3