Question

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.

a) Find the two-digit number which is 2 times the sum of its digits
b) Find the two-digit number which is greater than the product of its digits by 26

Answer 1

Part a) The number is 18

Part b) The number is 32

Explanation:

Let

x ----> tens digit

y ---> unit digits

N ----> the number (xy)

Part a) Find the two-digit number which is 2 times the sum of its digits

we know that

The number is equal to

`N=10x+y` ----> equation A

Remember that

The two-digit number is 2 times the sum of its digits

so

`N=2(x+y)` -----> equation B

equate equation A and equation B

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

`10x-2x=2y-y`

`y=8x`

The only single-digit values for x and y that satisfy the requirements are

x=1, y=8

therefore

The number is 18

Part b) Find the two-digit number which is greater than the product of its digits by 26

we know that

The number is equal to

`N=10x+y` ----> equation A

Remember that

The two-digit number is greater than the product of its digits by 26

so

`N=xy+26` -----> equation B

equate equation A and equation B

`10x+y=xy+26`

Subtract xy from each side

`10x+y-xy=26`

Factor -y

`10x-y(x-1)=26`

X must be bigger than 2 or we cannot get 26

Let x=3

`10(3) -y(3-1) =26`

`30 -2y = 26`

Subtract 30 from each side

`-2y = -4`

Divide by -2 both sides

`y=2`

therefore

The number is 32