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9. CCSS MODELING Refer to the table at
the right.

a. Write equations that represent the cost of printing digital photos at each lab.

b. Under what conditions is the cost to print digital photos the same at both stores?

c. When is it best to use EZ Online Digital Photos and when is it best to use the local store?

9 CCSS MODELING Refer to the table at the right a Write equations that represent the cost of printing digital photos at each lab b Under what conditions is the class=

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rvkacademic

Answer:

a)

  • CO = 0.15x + 2.70  for online store
  • CL = 0.25x for local store

b)

  • When the number of photos printed = 27 then the cost is the same at both stores

c)

  • When number of photos printed exceeds 27, the online store is cheaper
  • When number of photos printed is less than 27, the local store is cheaper

Step-by-step explanation:

Let x represent the number of photos being printed at either store

Let's write equations for cost of printing at both stores

a)
CO = 0.15x + 2.70  for online store
CL = 0.25x for local store

b)
Cost of printing is the same when CO = CL
or
0.15x + 2.70 = 0.25x
=> 0.25x =  0.15x + 2.70  (switch sides)
⇒ 0.25x - 0.15x = 2.70    (subtract 0.15x both sides)
⇒ 0.10x = 2.70                 (simplify above)
⇒ x = 2.70/0.10               (divide both sides by 0.10)
⇒ x = 27                          (simplify)

Therefore when the number of photos printed = 27 then the cost is the same at both stores

c)
It is best to use the online store when the online cost is less than local cost

CO < CL
⇒ 0.15x + 2.70 < 0.25x
⇒ 0.25x > 0.15 > 2.70      (switch sides, inequality changes direction
⇒ 0.10x > 2.70                  (simplify using process in part b)
⇒  x > 27                           (divide by 0.10 both sides and simplify)

So when number of photos printed exceeds 27, the online store is cheaper

When number of photos printed is less than 27, the local store is cheaper

Let's verify
Take x = 30 > 27
CO = 0.15(30) + 2.70 = $7.20
CL = 0.25(30) = $7.50
so online store cheaper

Take x = 20 < 27
CO = 0.15(20) + 2.7 = $5.70
CL = 0.25(20) = $5.00  
so local store is cheaper



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