Question

Sum of two numbers is 29 and one number exceeds another by 5.Find the numbe

Answer 1

• Let the greater number be x.

• Let the smaller number be y.

By data,

Sum of the two numbers is 29.

x + y = 29.

Let the above equation be equation 1.

Again by data,

One number exceeds the another by 5.

This means greater number exceeds the smaller number by 5.

x = y + 5

x - y = 5

Let the above equation be equation 2.

Adding equations 1 and 2.

$x + y = 29 \\ \\ x - y = 5 \\ \\ on \: adding \\ \\( x + y) + (x - y) = 29 + 5 \\ \\ x + y + x - y = 34 \\ \\ 2x = 34 \\ \\ x = \dfrac{34}{2} \\ \\ x = 17$

The greater number is 17.

Substitute x = 17 in any one of the equations.

Let's substitute the value of x in 2nd equation.

$x - y = 5 \\ \\ 17 - y = 5 \\ \\ 17 - 5 = y \\ \\ y = 17 - 5 \\ \\ y = 12$

The smaller number is 12.

ANSWERS:

• The greater number is 17.
• The smaller number is 12.

Answer 2

Answer:

Given :-

• Sum of two numbers = 29
• On exceeds another by 5

To Find :-

Number

Solution :-

Let the smaller number be x and greater number be x + 5

$\tt \implies \:( x + \{x + 5 \}) = 29$

$\tt \implies \: (x + x + 5) = 29$

$\tt \implies \: 2x + 5 = 29$

$\tt \implies \: 2x = 29 - 5$

$\tt \implies \: 2x = 24$

$\tt \implies \: x \: = \cancel{\dfrac{24}{2} }$

${\frak {}\fbox\red{x = 12}}$

Numbers are

$\sf \: x = 12$

$\sf \: x + 5 = 12 + 5 = 17$

Verification

12 + (12 + 5 )= 29

12 + 17 = 29

29 = 29