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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

Respuesta :

calculista

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

[tex]N=10x+y[/tex] ----> equation A

Remember that

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

so

[tex]N=2(x+y)[/tex] -----> equation B

equate equation A and equation B

[tex]10x+y=2(x+y)[/tex]

[tex]10x-2x=2y-y[/tex]

[tex]y=8x[/tex]

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

[tex]N=10x+y[/tex] ----> equation A

Remember that

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

so

[tex]N=xy+26[/tex] -----> equation B

equate equation A and equation B

[tex]10x+y=xy+26[/tex]

Subtract xy from each side

[tex]10x+y-xy=26[/tex]

Factor -y

[tex]10x-y(x-1)=26[/tex]

X must be bigger than 2 or we cannot get 26

Let x=3

[tex]10(3) -y(3-1) =26[/tex]

[tex]30 -2y = 26[/tex]

Subtract 30 from each side

[tex]-2y = -4[/tex]

Divide by -2  both sides

[tex]y=2[/tex]

therefore

The number is 32

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