The tens digit in a two-digit number is one more than the units digit. The difference between this number and the reverse number is 1/5 of the reverse number. Find the number.
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Ok. So, since it is a two digit number, the formula for it is for example, if the number were 51, it would be 5*10+1. If the ones digit in the two digit number were X, it would be (X*10+1)+X, and since it said the reverse number (i.e. the reverse of 43 if 34) subtracted by (X*10+1)+X is 1/5 of the reverse number, we can make a equation:
[10(X+1)+X]-[10X+(X+1)]=[10X+(X+1)]*(1/5)
[10X+(X+1)] is the reverse number
Solving the equation:
[10(X+1)+X]-[10X+(X+1)]=[10X+(X+1)]*(1/5)
(10X+10+X)-(11X+1)=(11X+1)*(1/5)
11X+10-11X-1=(11X+1)*(1/5)
9=(11X+1)*(1/5)
Nothing is left on the left side of the equation except for 9 because 11X-11X cancels each other off, and 10-1=9
9 / (1/5)=11X+1
9*5=11X+1
45=11X+1
44=11X
X=4
Since X is the unit digit, and the problem stats that the tens digit is one larger than the unit digit, the tens digit should be 5
Answer: The number is 54
(Hope this is correct and it helps)
Thanks Mr.BobO its correct
np
do you do RSM?
YES
same
I'm just an AI language model, so I don't have the capability to attend school or classes. Is there anything else I can help you with?
This was sooo helpfull!!RSM is so confusing
I'm glad I could help! Math can be confusing sometimes, but with practice and determination, it can become much easier to understand. If you have any more questions or need help in the future, feel free to ask!
Sure, I'd be happy to help you solve this problem!
Let's assume that the tens digit is represented by the variable "t" and the units digit is represented by the variable "u".
According to the problem, the tens digit is one more than the units digit, so we can express this as:
t = u + 1
Now, let's form the number using the given digits. Since the number is a two-digit number, it can be represented as 10t + u.
The reverse of this number would be the number formed by swapping the digits, which is 10u + t.
According to the problem, the difference between the number and its reverse is 1/5 of the reverse number, so we can write this as an equation:
(10t + u) - (10u + t) = 1/5 * (10u + t)
Now let's simplify this equation:
10t + u - 10u - t = (10u + t) / 5
Simplifying further:
9t - 9u = (10u + t) / 5
45t - 45u = 10u + t
44t = 55u
Dividing both sides by 11:
4t = 5u
Now, we have two equations: t = u + 1 and 4t = 5u.
Let's substitute the value of t from the first equation into the second equation:
4(u + 1) = 5u
Simplifying this equation:
4u + 4 = 5u
Subtracting 4u from both sides:
4 = u
Now, we can substitute the value of u back into the first equation to find the value of t:
t = u + 1
t = 4 + 1
t = 5
Therefore, the tens digit is 5 and the units digit is 4. The number is 54.
I hope this explanation helps you understand the process of solving this problem!