Can anyone solve these math questions?

Question

1. The units digit of a two-digit number exceeds its tens digit by 5. If the number is divided by the sum of its digits, the quotient is 3 and the remainder is 5. What is the number?

2. If a two-digit number is divided by its tens digit, the quotient is 12 and the remainder is 1. If the number with its digits interchanged is divided by its original units digit, the quotient is 10 and the remainder is 4. What is the original number?

Answer 1

1- 38
2- 48

Answer 2

1.Let the digit in the units place be x and in the tens place be y.
So, the number would be 10y+x.
x exceeds y by 5.So,
x=y+5 is the first equation.
Sum of the digits is x+y.
If the number is divided by the sum of its digits, the quotient is 3 and the remainder is 5. So,
3{x+y}+5=10y+x
3x+3y+5=10y+x
3x-x+3y-10y+5=0
2x-7y+5=0
2(y+5)-7y+5=0
2y+10-7y+5=0
2y-7y+10+5=0
-5y+15=0
-5y=-15
y=15/5
y=3
x=y+5
x=3+5
x=8
So, the number is 38.

2.Let the digit in the units place be x and in the tens place be y.
So the number is 10y+x.
If the number is divided by its tens digit, the quotient is 12 and the remainder is 1.So,
12y+1=10y+x
12y-10y-x+1=0
2y-x+1=0 is the first equation.
If the number with its digits interchanged , the number becomes 10x+y.
If the number with its digits interchanged is divided by its original units digit, the quotient is 10 and the remainder is 4. So,
10x+4=10x+y
10x-10x+4=y
y=4
From equation 1 we get,
2(4)-x+1=0
8+1-x=0
9-x=0
x=9
So, the original number is 49.

Answer 3

1)

The first sentence tells you the number must be one of

16, 27,38,49
in the same order, the sum of the digits is

7,9,11,13

7 into 16 goes 2 remainder 2.....no good

9 into 27 goes 3 with no remainder.....no good

11 into 38 goes 3 remainder 5.......now go back to the question and check the rules in the second sentence.

Have you found the answer yet?

Now you know the meaning of the word quotient.

Try the next one for yourself and if you can't do it, go back to your teacher

Answer 4

1 5
2 12

Answer 5

1 - 38
2 - 49