Ms. Taylor works at a music store. Last week she sold 6 more than 3 times the number of CDs that she sold this week. Ms. Taylor sold a total of 110 CDs over the 2 weeks. Write and solve a system of equations that can be used to find l, the number of CDs she sold last week, and t, the number of CDs she sold this week?

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answer:

(7 x + 6 y) (49 x^2 - 42 x y + 36 y^2)

discussion:

the trick is to recognize that 343 = 7^3 and 216 = 6^3 and, in general,

a^3 + b^3 =   (a + b) (a^2 - a b + b^2).

in our case

343x^3+216y^3   =   (7x)^3 + (6y)^3

so take a = 7x and b = 6y in the above equation to get the answer.

you,

mrb