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
