hello my name is zoe and I am a student. This a a middle grade quesion

at the last school election in Angletown 4620 votes were cast. Candidate Acute received 236 more votes than Candidate Obtuse. Candidate Right received 698 votes more than Candidate Acute. Candidate Straight received 256 votes less than Candidate Right. How many votes did each receive?

The four candidates are Acute, Obtuse, Right and Straight. I am goint to use the first letter in each candidate's name to stand for the number of votes that he or she received. Thus the four facts I know are

1. A + O + R + S = 4620
   
   
2. A = O + 236
   
   
3. R = A + 698
   
   
4. S = R - 256

Equation 1. has four letters in it and my goal is to find a way to write equation 1. with only one letter in it. Then I can solve for that letter. My plan is as follows:

• Equation 4. will allow me to replace the S in equation 1. by R - 256 and thus have equation 1. with only the letters A, O and R.
  
  
• Equation 3. will allow me to replace the R in this new form of equation 1. by A + 698 and thus have equation 1. with only the letters A and O in it.
  
  
• Finally equation 2. will allow me to replace the A in equation 1. by O + 236 to have only the letter O remaining.

• A + O + R + S = 4620
  thus
  A + O + R + R - 256 = 4620
  or
  A + O + 2R - 256 = 4620
  
  
• A + O + 2R - 256 = 4620
  thus
  A + O + 2(A + 698) - 256 = 4620
  hence
  3A + O + 1146 = 4620
  
  
• 3A + O + 1146 = 4620
  hence
  3(O + 236) + O + 1146 = 4620
  thus
  4O + 1848 = 4620

Solve for O and then use equations 2., 3. and 4. to find A, R and S. When you are done check to seethat the total of all the votes is 4620.