Question

The sum of two numbers is 80. The greater number is
11 more than twice the smaller number. Find both
the numbers.

Answer 1

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Let us assume, x and y are the two numbers and x > y

The sum of two numbers is 80.

[tex] x + y = 80--1[/tex]

The greater number is  11 more than twice the smaller number.

[tex] x = 2y + 11 ----2 [/tex]

Substitute the value of x from equation 1 in equation 2

2y + 11 + y = 80

3y + 11 = 80

3y = 69

[tex]\boxed{y = 23 }[/tex]

Therefore, x = 2y + 11 = (2 * 23) + 11 = 57

$\boxed{x=57}$

The two numbers are 57 and 23