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Question

Peter had three piles of pickled peppers. He has a total of 52 pickled peppers. His second pile has seven more peppers than the first pile. His third pile has three fewer than the first. Write and solve an equation to find out how many in each pile. Show work.

Answer 1

Sherry S is correct, but for this problem there really wasn't any need for 3 variables.

 

Pile 1:  x

Pile 2 (7 more):  x + 7

Pile 3 (3 less):  x-3

 

x + x+ 7 + x - 3 = 52

Add the variables and numbers

3x + 4 =52

subtract 4 from both sides

3x = 48

divide both sides by 3

x = 16

x+7 = 23

x-3 = 13

 

Your piles have 16, 23, and 13 peppers respectively.

Answer 2

x= pile one          y= pile two      z= pile three

 

He has a total of 52 pickled peppers.

x + y + z = 52

 

His second pile has seven more peppers than the first pile.

y = x + 7

 

His third pile has three fewer than the first

z = x - 3

 

To solve for x, use the first equation and substitute (x+7) for y and (x-3) for z

x + y + z = 52

x + (x+7) + (x-3) = 52

3x + 4 = 52

      -4    -4

3x    = 48

/3          /3

x   = 16

 

Now take your x=16 and substitute it into the other two equations

 

y = x + 7

y = 16 + 7

y = 23

 

z = x - 3

z = 16 - 3

z = 13

 

The piles have 16, 23, and 13 respectively.

 

CHECK IT!

   x  +  y  +  z  = 52

? 16 + 23 + 13 = 52

?      39   + 13 = 52

Yes!