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Rus_ich [418]
4 years ago
11

In a two-digit number the tens digit is four less than the units digit. Seven times the tens digit plus five times the units dig

it is equal to 56. Find the digits.
Mathematics
1 answer:
Iteru [2.4K]4 years ago
3 0

The digits of the number are 7 and 3

Step-by-step explanation:

In a two-digit number:

  • The tens digit is four less than the units digit
  • Seven times the tens digit plus five times the units digit is equal to 56

We need to find the digits

Assume that the unit digit is x and the ten digit is y

∵ x represents the unit digit

∵ y represents the ten digit

∵ The ten digit is four less than the unit digit

- That means subtract 4 from the unit digit to get the ten digit

∴ y = x - 4 ⇒ (1)

∵ Seven times the tens digit plus five times the units digit is

   equal to 56

- That means multiply the ten digit by 7 and the unit digit by

   5 and add the two products and equate the sum by 56

∴ 7y + 5x = 56 ⇒ (2)

Now we have a system of equations to solve it

Substitute y in equation (2) by equation (1)

∵ 7(x - 4) + 5x = 56

- Simplify the left hand side

∴ 7x - 28 + 5x = 56

- Add the like terms in the left hand side

∴ 12x - 28 = 56

- Add 28 to both sides

∴ 12x = 84

- Divide both sides by 12

∴ x = 7

- Substitute the value of x in equation (1) to find y

∵ y = 7 - 4

∴ y = 3

∴ The number is 37

The digits of the number are 7 and 3

Learn more:

You can learn more about the system of equation in brainly.com/question/6075514

#LearnwithBrainly

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