Is this right I need some help with this Please Alg1?

Question

Mrs. Apple accidentally reversed the digits of a test and shorted the student 36 points. Mrs.Apple told the student that the sum of the digits was 14 and agreed to give the student his correct score plus extra credit if he could determine his actual score with out looking at his test. What was his actual score on the test?

I did this

x-36y=14(line1)

x+y=63(line2)

Then I would do this

x-36=14 (line1)

36x+36y=2268 (line 2 by multiplying the whole line by 36 to cross out the ys)

I think I messed up and have got my numbers mixed up b/c I cant get an answer..Can you help? Thanks

Answer 1

Let the orginal score be a two digit number ab.

We can write this 10a + b.

The new score is ba (digits reversed) and can be written as 10b + a.

We also know that a + b = 14.

The difference between the original and new score is 36 so;

(10a + b) - (10b + a) = 36

10a + b - 10b - a = 36

9a - 9b = 36

a - b = 4

Rearrange to get a = 4 + b

Substitute into a + b = 14 to get

                      4 + b + b = 14

                      4 + 2b = 14

                            2b = 10

                              b = 5

As a + b = 14, then a = 9.

So the original score was 95.

Answer 2

Let X represent 10s digit and Y 1s digit of correct score.

Actual score = X*10 + Y

Since digits got reversed, wrong score = Y*10 + X

Actual score = wrong score + 36

X*10 + Y = (Y*10 + X) + 36

X*9 = Y*9 + 36                           equation 1

Also given, digits add up to 14

X + Y = 14                                 equation 2

Substituting eqution 2 into 1 get:

X*9 = 9(14 - X) + 36

X*9 = 126 - X*9 + 36

X*18 = 162

X = 9

Therefore Y = 5