Question

14.Three times a number increased by five times another number is 49, but twice the second
number exceeds five times the first number by 1. What are the numbers?

Answer 1

Answer:

The two numbers are 3 and 8.

Step-by-step explanation:

Given :-

• Three times a number increased by 5 times another number is 49.
• Twice the second number exceeds 5 times the first number by 1.

To find :-

• The two numbers.

Solution :-

Let the 1st number be x and the 2nd number be y.

According to the 1st condition :-

• Three times a number increased by 5 times another number is 49.

$\implies \sf \: 3x + 5y = 49..........(i)$

According to the 2nd condition :-

• Twice the second number exceeds 5 times the first number by 1.

$\implies \sf \: 2y - 5x = 1 \\ \\ \implies \sf \: - 5x + 2y = 1.........(ii)$

Now multiply eq(i) by 5 and eq(ii) by 3.

• 15x+25y = 245...............(iii)
• -15x+6y=3................(iv)

Now add eq(iii) and eq(iv), we get,

15x+25y-15x+6y=245+3

→ 31y = 248

→ y = 248/31

→ y = 8

• 2nd number = 8

Now put y = 8 in eq(ii) for getting the value of x.

-5x+2y=1

→ -5x+2×8=1

→ -5x+16=1

→ -5x =1-16

→ -5x = - 15

→ x = -15/-5

→ x = 3

• 1st number = 3

Answer 2

Answer:

The required two numbers are 8 and 3.

Step-by-step explanation:

Let the first number be x and second number be y.

• Three times a number increased by five times another number is 49 :]

➳ 3x + 5y = 49 ............[Equation (i)]

• Twice the second number exceeds five times the first number by 1 :]

➳ 2y = 5x + 1

➳ 5x - 2y = -1 ............[Equation (ii)]

Now, Multiplying equation (i) by 5 we get,

➳ 15x + 25y = 245 ...........[Equation (iii)]

Multiplying equation (ii) by 3 we get,

➳ 15x - 6y = -3 ............[Equation (iv)]

Now, substracting equation (iv) from equation (iii) we get ,

➳ 31y = 248

➳ y = 248/31

➳ y = 8

Putting value of y = 8 in equation (i) we get,

➳ 3x + 5y = 49

➳ 3x + 5(8) = 49

➳ 3x + 40 = 49

➳ 3x = 49 - 40

➳ 3x = 9

➳ x = 9/3

➳ x = 3