SOLUTION: In a two-digit number, 5 times the units digit added to the tens digit equals 43. Five times the tens digit added to the units digit equals 47. Find the number
Question 1146954: In a two-digit number, 5 times the units digit added to the tens digit equals 43. Five times the tens digit added to the units digit equals 47. Find the number
You can put this solution on YOUR website! let x = the value of the tens digit.
let y = the value of the ones digit.
the number is 10x + y.
example: in the number 57, 5 is the value of the tens digit and 7 is the value of the ones digit and the number is 10 * 5 + 7 = 57.
this is because each tens digit is worth 10 units while each units digit is worth 1 unit.
your equations are:
x + 5y = 43
5x + y = 47
multiply both sides of the first equation by 5 and leave the second equation as is to get:
5x + 25y = 215
5x + y = 47
subtract the second equation from the first to get:
24y = 168
solve for y to get:
y = 7
replace y with 7 in the second equation of 5x + y = 47 to get:
5x + 7 = 47
subtract 7 from both sides to get:
5x = 40
solve for x to get:
x = 8
replace x with 8 and y with 7 in both original equqations to get:
x + 5y = 43 becomes 8 + 35 = 43 which becomes 43 = 43 which is true.
5x + y = 47 becomes 40 + 7 = 47 which becomes 47 = 47 which is true.
both original equation are true when x = 8 and y = 7.
your number is 10x + y which is equal to 87.
that's your solution.
Let x be the ones digit and y be the tens digit.
5x + y = 43 (1)
x + 5y = 47 (2)
Add the equations. You will get
6x + 6y = 43 + 47 = 90
x + y = 90/6 = 15. (3)
Express x = 15 - y and substitute it into equation (1). You will get
5*(15-y) + y = 43
75 - 5y + y = 43
-4y = 43 - 75 = -32
y = = 8.
Then from (3) x = 15-y = 15-8 = 7.
ANSWER. The number is 87.
