Let the units digit = x
Let the 10s digit = y
Equations
10y + x - 2 = 8 * (x + y) (1)
10y + x - 54 = 10x + y (2)
Equation 1
10y + x - 2 = 8 * (x + y) Remove the brackets on the right
10y + x - 2 = 8x + 8y Subtract 8y from both sides
10y - 8y + x - 2 = 8x Subtract 8x from both sides
2y + x - 8x - 2 = 0 Combine
2y - 7x - 2 = 0 (3)
Equation 2
10y + x - 54 = 10x + y Subtract 10x
10y - 9x - 54 = y Subtract y from both sides.
9y - 9x - 54 = 0 Divide by 9
y - x - 6 = 0 Multiply by 2
2y - 2x - 12 = 0 (4)
Solution
Subtract (3) - (4)
2y - 7x - 2 = 0
2y - 2x - 12 = 0
- 5x + 10 = 0 Subtract 10 from both sides.
- 5x = - 10 Divide by - 5
x = 2
Use (4) to find y
2y - 2x - 12 = 0 Let x =2
2y - 2(2) - 12 = 0 Remove the brackets
2y - 4 - 12 = 0 Combine
2y - 16 = 0 Add 16 to both sides.
2y = 16 Divide by 2
y = 8
Answer 82
I'll leave the check to you, but the answer of 82 is correct.
