Applications to systems

Question

The sum of two numbers is 27. The larger of the two numbers is 7 less than triple the smaller number indicate the two numbers below

smaller number

larger number

Answer 1

Let x represent the smaller number

Let y represent the larger number

 

The sum of two numbers is 27.

 

Implies x + y = 27

 

The larger of the two numbers is 7 less than triple the smaller number

Implies 3x -7 = y

 

Now we have a system of linear equation with two variables (Solve by Graphing, Substitution, Elimination Methods)

 

I will solve this via Substitution Method

 

x + y = 27

3x -7 = y

 

x + (3x - 7) = 27

Combine like terms

4x - 7 = 27

Add 7 to both side of the equation

4x = 34

Divide by 4

 

x = 8.5

 

If x = 8.5 and y = 3x -7 = 3(8.5)-7 = 18.5

Thus x = 8.5 and y = 18.5

 

 

 

We can double check our answer :

 

8.5 + 18.5 = 27  check

And

3(8.5)-7 = 18.5