Question

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))?

Answer 1

6 Dollars.

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)