A maple syrup producer has a booth at a Sunday farmer's market. The producer sells organic maple syrup by the pint. To get customers to start buying more pints of organic maple syrup, the producer is trying out a new discount system. Customers buying more than two pint bottles will get a discount per pint, beginning with the third pint bottle. For these customers, the expression shown represents the total price, in dollars, of buying p pints of organic maple syrup. 29.50 + 13.50(p – 2)

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MrRoyal MrRoyal · Answer 1 · 2021-03-27T16:59:29+01:00

Answer:

See Explanation

Step-by-step explanation:

Given

[tex]Price = 29.50 + 13.50(p - 2)[/tex]

The question has missing details. However, I will solve on a general term.

A possible question could be to find the cost of purchasing (say 10 bottles).

To do this, we simply substitute 10 for p.

So:

[tex]Price = 29.50 + 13.50(p - 2)[/tex]

[tex]Price = 29.50 + 13.50(10 - 2)[/tex]

[tex]Price = 29.50 + 13.50 * 8[/tex]

[tex]Price = 29.50 + 108[/tex]

[tex]Price = 137.50[/tex]

i.e. $137.50 for 10 pint bottles

Another possible question is to calculate the number of pint bottles that amount to (say $70).

To do this, we simply substitute 70 for Price.

So:

[tex]Price = 29.50 + 13.50(p - 2)[/tex]

[tex]70 = 29.50 + 13.50(p - 2)[/tex]

Collect like terms

[tex]70 - 29.50 = 13.50(p - 2)[/tex]

[tex]40.5= 13.50(p - 2)[/tex]

Divide both sides by 13.50

[tex]3= p - 2[/tex]

Add 2 to both sides

[tex]3 + 2 = p - 2 + 2[/tex]

[tex]5 = p[/tex]

[tex]p = 5[/tex]

i.e. $70 will buy 5 pint bottles

Use this explanation to find solution to your question