The answer in the back of the book is wrong?

Question

If Y is your before-tax income, suppose that the government takes away 1/4 Y-10 as taxes. What was your pre-tax income if your after-tax income is $280?                  Here is my set-up; 4(1/4 Y -10=280)                                                                                                                                                                                                         Y-40 =1120                                                                                                                                                                                                      Y=1160              1/4 (1160)= $290 is the pre-tax income.                         The answer in the back of the book is Y= $360.   I do not know if I read the question wrong, but I reread it. And I  try to also to let Y be 280 and then solve the equation. The answer is wrong, too. And I did the set-up three times, I arrive at the same answer. The problem is straight forward. Did I miss a step?

Answer 1

The correct answer is $360.

After tax we have Y-(¼Y-10)=280,

¾Y+10=280,

¾Y=270,

Y=4×270/3=4×90=$360.

CHECK: 360/4=$90, less $10=$80. This is tax deducted, so after tax $360 becomes 360-80=$280.