How do I solve this story problem?
2016-06-20 6:52 pm
How do I solve? Four times the ones digit of a positive, two-digit integer is 1 greater than the tens digit. Reversing the digits decreases the number by 45. What is the number?
回答 (2)
2016-06-20 7:06 pm
Let a be the tens digit, and b be the ones digit.
4b - a = 1 ...... [1]
10b + a = (10a + b) - 45 ...... [2]
From [1] :
a = 4b - 1 ...... [3]
From [2] :
10b + a = 10a + b - 45
9b - 9a = -45
b - a = -5
a = b + 5 ...... [4]
[3] = [4] :
4b - 1 = b + 5
3b = 6
b = 2
Substitute b = 2 into [4] :
a = 2 + 5
a = 7
Answer : The number is 72.
4b - a = 1 ...... [1]
10b + a = (10a + b) - 45 ...... [2]
From [1] :
a = 4b - 1 ...... [3]
From [2] :
10b + a = 10a + b - 45
9b - 9a = -45
b - a = -5
a = b + 5 ...... [4]
[3] = [4] :
4b - 1 = b + 5
3b = 6
b = 2
Substitute b = 2 into [4] :
a = 2 + 5
a = 7
Answer : The number is 72.
2016-06-20 6:57 pm
You have a number: yx
4x = y + 1
4x - 1 = y
x = 1 , y = 3
x = 2 , y = 7
No other possibilities for x and y
31 , 72 are your possible numbers
13 , 27 are the numbers we get when the digits are reversed
31 - 13 = 18
72 - 27 = 45
72
4x = y + 1
4x - 1 = y
x = 1 , y = 3
x = 2 , y = 7
No other possibilities for x and y
31 , 72 are your possible numbers
13 , 27 are the numbers we get when the digits are reversed
31 - 13 = 18
72 - 27 = 45
72
收錄日期: 2021-04-18 15:08:04
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