Use an equation to solve for the five numbers.

Question

The sum of the five numbers is 50. The first number is half of the second number. The third number is twice the second number. The fourth number is five less than the second number. The fifth number is the same as the second number.

Needs to include an equation to solve for all five numbers. 

Answer 1

Let 1st number = a

Let 2nd number = b

Let 3rd number = c

Let 4th number = x

Let 5th number = y

 

Use these variables to establish equations based on the problem.  Set these equations in order of each statement that correspond.

 

a + b + c + x + y = 50                              eq1

a = (1/2)b                                                eq2

c = 2b                                                      eq3

x = b - 5                                                  eq4

y = b                                                       eq5

 

So we have 5 variables with 5 equations.  What we need to do next is perform substitution to get a single equation that contains only one variable.  We look at the equations and see what we can substitute on at a time.

 

Notice that every equation listed here are in terms of b.  So lets get eq1 only in terms of b.

 

a + b + c + x + y = 50      becomes

 

(1/2)b + b + (2b) + (b - 5) + b = 50

 

 

Since we have a denominator in one of the terms, multiply both sides of the equation  by 2.

 

b + 2b + 4b + 2(b - 5) + 2b = 100

 

b + 2b + 4b + 2b - 10 + 2b = 100

 

11b = 110

 

 

Divide both sides of the equation by 11.

 

b = 10

 

 

Now you just substitute this value of b into eq2 - eq5 to find the other numbers.

 

 

Answer 2

First: ½(x)

Second: x

Third: 2x

Fourth: x-5

Fifth: x

 

Add these five expressions up and say that = 50.  DONE!