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Question

In the base ten number system the number 526 means 5 10^2+2 10 + 6. In the Land of Mathesis, however, numbers are written in the base r. Jones purchases an automobile there for 440 monetary units (abbreviated m.u). He gives the salesman a 1000 m.u bill, and receives, in change, 340 m.u. The base r is:

Accepted Answer

If Jones received 340 m.u. change after paying 1000 m.u. for something that costs 440 m.u., then 440_r + 340_r = 1000_r This equation can be rewritten as 4r^2 + 4r + 3r^2 + 4r = r^3 Bring all of the terms to one side to get r^3 - 7r^2 - 8r = 0 Factor to get r(r-8)(r+1)=0 Since base numbers are always positive, base r is 8, which is answer choice 8.