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

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

----> equation A

Remember that

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

so

-----> equation B

equate equation A and equation B

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

----> equation A

Remember that

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

so

-----> equation B

equate equation A and equation B

Subtract xy from each side

Factor -y

X must be bigger than 2 or we cannot get 26

Let x=3

Subtract 30 from each side

Divide by -2  both sides

therefore

The number is 32

13875138answer:

step-by-step explanation:

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d) 30 units^2

area of rectangle = l × b

we know,

length = 10 unit

breadth = 3 unit

applying the formula,

= l × b

= 10 × 3

= 30 unit^2

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