Shorthand Notation

We can devise a shorthand notation for large numbers by letting d_n stand for the occurrences of n consecutive ds where n is a positive integer and d is a fixed digit between 0 and 9. So, 1_49_58_23_6 would denote the number 11119999988333333. Find the ordered triple (x,y,z) such that 2_x3_y5_z+3_p5_q2_r=5_37_28_35_17_3.
Source: NCTM Mathematics Teacher, December 2005

SOLUTION
We write out the final sum in regular notation as follows
2_x3_y5_z+3_p5_q2_r=555778885777
555+222=777
3+2=5
333+555=888
22+55=77
222+333=555
In summary,
222223333555
333555552222
——————–
555778885777
In shorthand notation,
2_53_45_3+3_35_52_4=5_37_28_35_17_3
(x,y,z)=(5,4,3)

Answer: (5,4,3)

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About mvtrinh

Retired high school math teacher.
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