Difference between revisions of "1961 AHSME Problems/Problem 17"
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In the base ten number system the number <math>526</math> means <math>5 \times 10^2+2 \times 10 + 6</math>. | In the base ten number system the number <math>526</math> means <math>5 \times 10^2+2 \times 10 + 6</math>. | ||
In the Land of Mathesis, however, numbers are written in the base <math>r</math>. | In the Land of Mathesis, however, numbers are written in the base <math>r</math>. | ||
− | + | Jones purchases an automobile there for <math>440</math> monetary units (abbreviated m.u). | |
He gives the salesman a <math>1000</math> m.u bill, and receives, in change, <math>340</math> m.u. The base <math>r</math> is: | He gives the salesman a <math>1000</math> m.u bill, and receives, in change, <math>340</math> m.u. The base <math>r</math> is: | ||
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==Solution== | ==Solution== | ||
− | If | + | If Jones received <math>340</math> m.u. change after paying <math>1000</math> m.u. for something that costs <math>440</math> m.u., then |
<cmath>440_r + 340_r = 1000_r</cmath> | <cmath>440_r + 340_r = 1000_r</cmath> | ||
This equation can be rewritten as | This equation can be rewritten as |
Latest revision as of 00:50, 7 June 2018
Problem
In the base ten number system the number means . In the Land of Mathesis, however, numbers are written in the base . Jones purchases an automobile there for monetary units (abbreviated m.u). He gives the salesman a m.u bill, and receives, in change, m.u. The base is:
Solution
If Jones received m.u. change after paying m.u. for something that costs m.u., then This equation can be rewritten as Bring all of the terms to one side to get Factor to get Since base numbers are always positive, base is , which is answer choice .
See Also
1961 AHSC (Problems • Answer Key • Resources) | ||
Preceded by Problem 16 |
Followed by Problem 18 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 • 26 • 27 • 28 • 29 • 30 • 31 • 32 • 33 • 34 • 35 • 36 • 37 • 38 • 39 • 40 | ||
All AHSME Problems and Solutions |
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