6. If y = 2q = 15, q + 2p = 5 and p + 2y = 7, then find the value of p + q + y.

Correct answer:

9: Right! But I hope you didn't go through the tedium of substitution and solving for q, p, and y. You are not asked for the values of each of the variables. Use Strategy 13, p. 100; BASIC SKILL - Mini Math Refresher - Equations, p. 158, Math Refresher (407), p. 244:

When you have two or more equations, it is sometimes easier to just add or subtract them to get a result. Add equations, then divide by 3.

      y + 2q = 15
      q + 2p =  5
  +   p + 2y =  7

------------------------------
 
  3q + 3p + 3y = 27

Factor 3: 3(q + p + y) =27; q + p + y = 9.

Incorrect answers:
Did you answer 27? Did you just add 15 + 5 + 7 to get 27? That really is kind of sloppy.
Use Strategy 13, p. 100; BASIC SKILL - Mini Math Refresher - Equations, p. 158, Math Refresher (407), p. 244:

Don't worry about going through the tedium of substitution and solving for q, p, and y. You are not asked for the values of each of the variables. When you have two or more equations, it is sometimes easier to just add or subtract them to get a result. Add equations, then divide by 3.

      y + 2q = 15
      q + 2p =  5
  +   p + 2y =  7

------------------------------
 
3q + 3p + 3y = 27

Factor 3: 3(q + p + y) =27; q + p + y = 9.

For all other answers:
No.Use Strategy 13, p. 100; BASIC SKILL - Mini Math Refresher - Equations, p. 158, Math Refresher (407), p. 244:

Don't worry about going through the tedium of substitution and solving for q, p, and y.
You are not asked for the values of each of the variables. When you have two or more equations, it is sometimes easier to just add or subtract them to get a result. Add equations, then divide by 3.

      y + 2q = 15
      q + 2p =  5
  +   p + 2y =  7

----------------------------

3q + 3p + 3y = 27

Factor 3: 3(q + p + y) =27; q + p + y = 9