need help on story problem for 8th grade math

Question

1-Mrs. fairbourn went to kneaders to buy some bread. The apple bread cost $5 more than the pumpkin spice. Orange rolls were $8 less than the apple bread. Freshly baked whole wheat was twice as much as the orange rolls. If Mrs. Fairborn spent $38.50, how much was each type of bread?


2- Mallory collected 3 times as many books as Claire. Nikki collected 2 books more than Mallory. Brad collected at 6 books less than Nikki. How many books did each person collect if the total number of books they collected was 44?

Answer 1

1.  First let's decide on variables to represent the cost of each type of bread.
     A = Apple bread,   P = Pumpkin Spice,  C = Orange rolls   W = Whole wheat
    Note:  I chose C for citrus rather than O for orange because O looks too much
              like a zero and will cause confusion.
    Let's set up equations from the information given.
 
  A = P + 5                 Apple bread cost $5 more than Pumpkin spice
  C = A - 8                  Orange Rolls are $8 less than apple bread
  W = 2C                     Whole wheat is twice as much as orange rolls
  A+C+P+W= 38.50     Mrs. Fairborn spent $38.50

From equation 1 and 2 we see that

C = A - 8

   = (P+5) - 8

   = P-3

 

W = 2C = 2(P-3) = 2P-6

 

We now have:  A = P + 5

                      C = P - 3

                      W = 2P -6

 

We can substitute those into the last equation  A+C+P+W = 38.50

 

(P+5) + (P-3) + P + (2P-6) = 38.50    drop parenthesis and combine like terms

5P - 4 = 38.50    Add 4 to both sides

5P = 42.50         Divide both sides by 5

P = 42.50/5

P = $8.50

 

We can now use the cost of P to find the other costs

 

A = P + 5 = $13.50

C = P - 3 = $5.50

W = 2P -6 = 17-6 = $11.00

 

Apple bread costs          $13.50

Pumpkin Spice costs      $ 8.50 

Orange rolls cost           $ 5.50

Whole Wheat costs        $11.00

                                  ----------

Total cost                     $38.50   

 

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For the 2nd problem we have the same basic logic

 

M = 3C                   Mallory collected 3 times as many books as Claire

N = M+2 = 3C+2    Nikki collected 2 more books than Mallory

B = N-6 = 3C+2-6 = 3C -4   Brad collected 6 books less than Nikki

 

M + N + C + B = 44    Total number of books collected was 44

 

Just as in problem 1, substitute the equivalent C value for each

variable in the last equation, solve for # of books Claire collected,

then work backwards for the rest:

 

3C + (3C + 2) + C + (3C-4) = 44

 

I'll leave the rest of this one to you to finish.  Good luck and God Bless.

 

Hope this helps and the logic isn't too confusing.  Good luck.