A tool set sells for $150 at a local hardware store. The tool set is on sale for 20% off the retail price, p, given by f (p) = 0.80p. Devon is interested in buying the tool set and has a coupon for $30 off the price of the tool set, which can be represented by g (p) = p - 30. What is the difference between the cost of using the coupon followed by the discount, f (g (p)), compared to using the discount followed by the application of the coupon, g (f (p)) ?

Question

Mathematics

Blaine Harrison

20 February, 11:02

A tool set sells for $150 at a local hardware store. The tool set is on sale for 20% off the retail price, p, given by f (p) = 0.80p. Devon is interested in buying the tool set and has a coupon for $30 off the price of the tool set, which can be represented by g (p) = p - 30. What is the difference between the cost of using the coupon followed by the discount, f (g (p)), compared to using the discount followed by the application of the coupon, g (f (p)) ?

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Shelby Wilkinson · Answer 1

6 Dollars.

Step-by-step explanation:

A toolset sells for $150 at a local hardware store. The toolset is on sale for 20% off the retail price, p, given by f (p) = 0.80p. Devon is interested in buying the toolset and has a coupon for $30 off the price of the toolset, which can be represented by g (p) = p - 30.

Therefore, the cost of using the coupon followed by the discount,

f[g (p) ] = 0.80 (p - 30) = 0.80 (150 - 30) = 96 dollars.

And the cost of using the discount followed by the application of the coupon,

g[f (p) ] = 0.80p - 30 = 0.80 * 150 - 30 = 90 dollars.

Therefore, the difference between f[g (p) ] and g[f (p) ] is (96 - 90) = 6 dollars. (Answer)