Write the statement for the problem in mathematical language. use x for the tens digit and y for the unit digits in the two digit numbers.

1) find the two-digit number which is 2 times the sum of its digits

2) find the two-digit number which is greater than the product of its digits by 26

1. 18

2. 32

Step-by-step explanation:

1.  xy  is the digit

Remember x is the 10 digit so we multiply it by 10

2(x+y) = x *10 +y

Distribute

2x+2y = 10x+y

Subtract y from each side

2x +2y -y = 10x +y - y

2x+y = 10x

Subtract 2x from each side

2x+y -2x = 10x-2x

y = 8x

Since these are digits x must be 1 or y would be bigger than a digit

Then y =8

Our two digit number is 18

2.  1.  xy  is the digit

Remember x is the 10 digit so we multiply it by 10

10x +y =xy+26

Subtract xy from each side

10x -xy + y = 26

Factor out an -y

10x -y(x-1) = 26

X must be bigger than 2 or we cannot get 26

Let x=3

30 -y(3-1) =26

30 -2y = 26

Subtract 30 from each side

-2y = -4

Divide by -2

y=2

The number is 32

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