complete question:
The sum of the digits of a two-digit numeral is 8. If the digits are reversed, the new number is 18 greater than the original number. How do you find the original numeral?
Answer:
The original number is 10a + b = 10 × 3 + 5 = 35
Step-by-step explanation:
Let
the number = ab
a occupies the tens place while b occupies the unit place. Therefore,
10a + b
The sum of the digits of two-digits numeral
a + b = 8..........(i)
If the digits are reversed. The reverse digit will be 10b + a. The new number is 18 greater than the original number.
Therefore,
10b + a = 18 + 10a + b
10b - b + a - 10a = 18
9b - 9a = 18
divide both sides by 9
b - a = 2...............(ii)
a + b = 8..........(i)
b - a = 2...............(ii)
b = 2 + a from equation (ii)
Insert the value of b in equation (i)
a + (2 + a) = 8
2a + 2 = 8
2a = 6
a = 6/2
a = 3
Insert the value of a in equation(ii)
b - 3 = 2
b = 2 + 3
b = 5
The original number is 10a + b = 10 × 3 + 5 = 35
75
Reduction of 12
3 x 4 = 12
Increase of 10
5 x 2 = 10
75 - 12 = 63
63 + 10 = 73
Change = 2 inches (75 - 73)
That's a quadratic, a nice parabola in vertex form.
The parabola has a positive x^2 term, so it's a CUP, concave up positive. It will have a minimum at the vertex, which is (2,5). Plot that point.
Now we need a couple of guide points to draw the usual parabola going up from both sides of its vertex. We try x=0 giving (0,9) and see that x=4 also gives 9, (4,9). Plot the parabola through those two points and the vertex and you're done.
