The value of a 2 digit number is 4 less than 6 times the sum of its digits.?

Question

If the digits of the number are reversed, the resulting number is 9 less than the original number. Find the number.

Answer 1

You need to write a system of equations and solve.

The value of a two digit number in the form XY is 10X + Y

10X + Y = 6(X+Y) - 4 for the first statement
10Y + X = 10X + Y - 9

Simplify each equation
the first becomes 4X - 5Y = -4
the second becomes -9X + 9Y = -9 or -X + Y = -1

If you solve the second for Y you get Y = X - 1
Substitute X - 1 into the first equation for Y and you get
4X -5(X-1) = -4
4X - 5X + 5 = -4
-X = -9
X = 9

Substitute to find Y
Y = X - 1
Y = 9 - 1
Y = 8

The original number is 98

Answer 2

Let's call the mystery number z. Let's suppose that one of the digits is x and the other is y (i.e. the 2 digit number is formed 'xy'). We know, then, that

6(x+y)-4=z

An interesting fact about reversing any two digit number is this: subtracting the two numbers is equal two 9 times the difference of the two digits. For example, if take the number 82. The reverse is 28. 82 less 28 is 54. 8 less 2 is 6, and 6 times 9 is 54! Thinking of this in reverse, if you knew the difference in numbers was 54, you would know (by dividing by 9) that the two digits were 6 numbers apart.

In the case above, the difference of the numbers is 9. Since 9/9 is 1, this means that x and y are one number apart (or consecutive). Another way to think of it is this:

y+ 1=x

(We know that y is the smaller number, because reversing x and y gives a smaller 2 digit number).

Substitute for x in the first equation:

6(y+1 +y)-4=z

6(2y+1)-4=z

12y+6-4=z

12y+2=z

At this point, you can graph it out. Notice, however, that another phenomenon of these numbers is that 10 times x plus y will give us the number (e.g. if the number was 63, then 10x6+3 gives us 63). Thus, we can see that

10x+y=z
10(y+1)+y=z
11y +10 =z

replace z above with 11y+10:

12y+2=11y+10

Thus,
12y-11y=10-2
y=8

Since

y+1=x

then

x=9.

The digit, therefore, is 98.

Answer 3

enable assujme numbet is interior this kind of 10x+y First condition - If the digits of the determination are reversed, the ensuing determination is 9 below the unique determination. 10x + y - (10y + x)=9 9x - 9y = 9 x - y = a million x = y + a million accessible mixture of numbers are xy 10 21 32 40 3 fifty 4 sixty 5 76 87 ninety 8 2d condition is =the cost of a 2 digit determination is 4 below 6 cases the sum of its digits 10x + y = 6 (x + y) -4 10x + y = 6x + 6y -4 4x + 4 = 5y y=4(x + a million)/5 because Y is interger, then (x+a million)/5 could be a million, 2, 3 because Y could be below <=9 (for 2 digit numbers), in reality accessible mixture are (x+a million)/5= a million or 2 For (x+a million)/5=a million ability x is 4 and y is 4, besides the undeniable fact that it does no longer fulfill condition a million. For (x+a million)/5=2 ability x is 9 and y is 8, which does fulfill condition a million. So answer is ninety 8. Bye

Answer 4

You need to write a system of equations and solve.

The value of a two digit number in the form XY is 10X + Y

10X + Y = 6(X+Y) - 4 for the first statement
10Y + X = 10X + Y - 9

Simplify each equation
the first becomes 4X - 5Y = -4
the second becomes -9X + 9Y = -9 or -X + Y = -1

If you solve the second for Y you get Y = X - 1
Substitute X - 1 into the first equation for Y and you get
4X -5(X-1) = -4
4X - 5X + 5 = -4
-X = -9
X = 9

Substitute to find Y
Y = X - 1
Y = 9 - 1
Y = 8

The original number is 98

Answer 5

2 digit number is given as 10x+y
According to the condition, a number is 4 less than 6 times the sum of its digits

10x + y=6(x+y) - 4
10x + y= 6x + 6y - 4
4x - 5y = -4 …(i)
if the digits are reversed, the resulting number is less than original number
10x+y = (10y+x) + 9

10x+y - (10y+x) =9
9x - 9y = 9
x – y = 1 ….(ii)

4x - 5y = -4
x – y = 1 multiply both sides by 5
5x - 5y = 5 …..(iii)
subtract equation (i) and (iii)
4x - 5y – (5x - 5y) = -4 - 5
-x = -9

x = 9

Now,

x – y = 1
9 – y = 1
y = 8
the number is 10x + y i.e. 10(9) + 8 = 90 + 8 = 98

Answer 6

You start with 10x + y = 6(x + y) - 4 and 10y + x = 10 x + y - 9 => (10 - 6)x + (1 - 6)y = -4 and -9x + 9y = -9 => 4x -5y = -4 and x - y = 9. Now solve for either "x" or "y" and substitute into one of the equations to get the second unknown. You have a system of linear equations, two equations in two unknowns. Manipulate the equations to eliminate the 'x" or the "y". Take it from there.

Answer 7

answer 44

a*10 +b = 6(a+b)-4 b*10+a =a*10+b -9
2 eqs 2 unknowns solv. it.

4a =5b-4
a= (5b-4)/4 4 must divide 5b
5b=20 => b=4 ,a=4 didn't see 2nd part
REDO

Answer 8

That is the MAIN reason the CALCULATOR was invented!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!