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

Answer:

Part a) The number is 18

Part b)  The number is 32

Step-by-step 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