Question 1124380: Hi, please help me solve this question:
SCRAP is a 5-digit number. The digits S,C,R,A, and P are used in these addition problems: A+A+A=CA and RS+RS+RS= PR
What number is scrap?
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website!
In order to solve this, one has to assume that two different letters cannot stand for the same digit.
Given that, we first look at A + A + A = CA, which is to say 3*A = CA.
Since the result is a two digit number, A must be larger than 3 because 3 times 3 is only 9. Also, A must be 9 or smaller because 9 is the largest single digit. Then looking at a multiplication table in the 3s column where the multiplier is 4 or larger, the only result where the second digit is the same as the multiplier is 3 X 5 = 15. Therefore A is 5 and C is 1.
Since 3 times RS is also a 2 digit number with two different digits, RS must be 32 or less because it can't be 33 and anything larger would have a result of three digits, and the smallest 2 digit number is 10 so it must be at least that. We want to find a multiple of 3 where the tens digit of the multiplier is the same as the ones digit of the product.
For multipliers with 1 as a tens digit, the only multiplier that qualifies is 17: 3 X 17 = 51. For multipliers with 2 as a tens digit, the only multiplier that qualifies is 24: 3 X 24 = 72. And for multipliers with 3 as a tens digit, the qualifier is 31: 3 X 31 = 93.
But we have already identified C = 1, so 17 and 31 are disqualified, so RS is 24 and PR is 72.
SCRAP = 41257
John
My calculator said it, I believe it, that settles it
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