The sum of three numbers is 80. The second number is one less than twice the first number. The third number is 37 more than the first number. Find the #'s

Question

Simple as it gets.

Answer 1

Let the first number = a

Let the second number = b

Let the third number = c

 

 

Set equations using these variables and the description.

 

a + b + c = 80                 eq1

b = 2a - 1                        eq2

c = a + 37                       eq3

 

 

We have 3 equations with 3 variables.  We will use a combination of elimination and substitution methods.  To find the variables.

 

 

Substitute eq2 and eq3 into eq1, since these two equations are in terms of a.

 

a + (2a - 1) + (a + 37) = 80

 

 

Solve for a from this equation.

 

a + 2a - 1 + a + 37 = 80

 

4a + 36 = 80

 

4a = 44

 

  a = 11

 

 

Substitute this value of a into eq2 and eq3.

 

b = 2(11) - 1

b = 22 - 1

b = 21

 

 

c = 11 + 37

c = 48

 

 

The three numbers are 11, 21, and 48.