# What are the integers a and b if their sum equals 57 and we know that b is 3 less than double of a?

Asked on by rogeryyo

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hala718 | High School Teacher | (Level 1) Educator Emeritus

Posted on

Given that the sum of the integers a and b is 57.

==> a + b= 57 ............(1)

We are given that b is 3 less than double a.

==> Then we will rewrite :

b= 2a - 3 ...............(2)

Now, using the substitution method, we will substitute (2) into (1).

==> a + (2a-3) = 57

==> 3a - 3 = 57

We will add 3 to both sides.

==> 3a = 60

==> a = 60/3 = 20

==> b= 2a-3 = 2*20 -3 = 40-3 = 37

==> Then the numbers are : a = 20 and b = 37.

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

The integers we have to determine are a and b .

Their sum is equal to 57

=> a + b = 57

b is 3 less than double the value of a

=> b = 2*a - 3

Substitute b = 2a - 3 in a + b = 57

=> 2a - 3 + a = 57

=> 3a = 60

=> a = 20

b = 57 - a = 37

The two integers are a = 20 and b = 37

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