Find the integer nearest to 1000 among integers which can be divided by 30 when 7 is added and can be divided by 45 when 8 is subtracted.
Answer
1043
Solution
When the integer which can be divided by 30 when 7 is added is written out, they are 23, 53, 83, -----.
Answer
1043
Solution
When the integer which can be divided by 30 when 7 is added is written out, they are 23, 53, 83, -----.
When the integer which can be divided by 45 when 8 is subtracted is written out, they are 53, 98, -----.
Thus, the least integer applicable to the conditions is 53.
Since the least common multiple of 30 and 45 is 90, the number to be found is expressed as 53 + 90 × X.
1000/90=11 with remainder 10.
53 + 90 × 10 = 953, 53 + 90 × 11 = 1043.
Therefore the integer nearest to 1000 is 1043.
