three consecutive intergers and found the product of 5 and the sum of the first two was 7 greater than the opposite of the third

Question

three consecutive intergers and found the product of 5 and the sum of the first two was 7 greater than the opposite of the third

 

Answer 1

Hi Kathi,
 
Translating story (word) problems into concise, precise math notation is a very important skill.  I hope you are getting good at it.
 
You should keep a table of what words mean.  For example,
      a,b,c    are consecutive, so                  c = b+1      b = a+1
      sum of a and b                                    a + b
      product of a and b                               a * b
       is                                                        =
     a is 2 greater than b                          a = 2 + b
     the opposite (negative) of a                   -a
Add to this chart every time you find a new phrase to translate.
 
Let a, b, and c represent  three consecutive integers (they are called variables and we want to know their values).
The sum of the first two is a + b  and the product of 5 and (the sum of the first two)  is
               5 * (a + b)   which also equals   5* (a + a+1)           because b can be replaced by a+1
 
Now, the expression we just found is 7 greater than the opposite of the third value:
 
     5 * (a  + a+1)  =  7 + (-c)      =  7 + (-(b+1))   =  7 + (-((a+1) + 1))     substituting, so WATCH SIGNS!
     5a + 5a + 5 = 7 -a - 2
     10a + a = 7 - 2 - 5
       11a = 0
 
Checking (this is very important):
    a = 0     b = 1  and    c = 2
the product of 5 and the sum of the first two numbers is 5 * (0 +1 ) = 5    which is
     5 = 7 + (-2)
Yep, that checks out!
 
    
 
 
 
 
 
 
 
 
 
 
 

Answer 2

x, x+1, and x+2 are the integers

5(x+x+1)=-(x+2)+7

5(2x+1)=-x-2+7

10x+5=-x+5

10x=-x

11x=0

x=0

x+1=1

x+2=2

0, 1, and 2 are the integers

5(0+1)=-2+7

5=5