contestada

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

Respuesta :

wegnerkolmp2741o

Answer:

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

To solve such problems we need to know about the number system.

The numbers are 18 and 32.

Given information,

  • x for the tens digit and y for the unit digits in the two-digit numbers.
  • tens digit = x,
  • ones digit = y,

Solution

1.)   The two-digit number, which is 2 times the sum of its digits.

We can write the statement as,

[tex]xy = 2 (x+y),[/tex]

As we know, it is already given that x is at tens place, so we can rewrite it as,

[tex](10\times x)+y = 2(x+y)\\10x +y = 2x + 2y\\10x - 2x = 2y - y\\8x = y\\\dfrac{y}{x} = \dfrac{8}{1}[/tex]

Thus, the number is in the ratio of 1:8. the only two numbers which satisfy such a ratio are 1 and 8 themselves. therefore, the number the two-digit number is 18.

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

We can write the statement as,

[tex]xy = (x\times y)+26[/tex],

As we know, it is already given that x is at tens place, so we can rewrite it as,

[tex]xy = (x\times y)+26\\(10 \times x) + y =(x\times y)+26\\\\10x + y = xy + 26\\10x + y - xy = 26\\10x + y(1-x) = 26[/tex]

doing hit and trial for the above equation, we get that if we take y greater than 2, we are not getting a whole number,

therefore, at y=2,

[tex]10x+y(1-x) =26\\10x+2(1-x)=26\\10x +2 -2x =26\\8x = 26-2\\8x = 24\\x = 3[/tex]

Hence, the number (xy) is 32.

Learn more about Numbers:

https://brainly.com/question/17429689

Otras preguntas