Cost of 2x number of roses is not double the cost of x number of roses.

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SUMMARY

The cost of six roses, represented by the equation C(r) = 2 + 5r, is not double the cost of three roses due to the fixed cost component of 2. When evaluating the expression C(2r) = 2C(r), substituting yields 2 + 5(2r) = 2(2 + 5r). Upon distribution, the left side simplifies to 2 + 10r, while the right side simplifies to 4 + 10r, confirming that the two sides are not equal. Thus, the cost does not scale linearly due to the fixed cost.

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Asawira Emaan
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Asalamoalikum,
Explain why the cost of six roses is not double the cost of three roses?

Hint: Think about a expression for cost of roses r, 2 + 5r.
What if the expression for cost was just 5r instead?
 
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For the first part of the problem, we are given:

$$C(r)=2+5r$$

And we are asked to determine if the following is true:

$$C(2r)=2C(r)$$

Or:

$$2+5(2r)=2(2+5r)$$

After you distribute, do you find this true?
 

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