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