2009 CEMC Pascal Problems/Problem 10

Problem

If $z = 4$ , $x + y = 7$ , and $x + z = 8$ , what is the value of $x + y + z$ ?

$\text{ (A) }\ 9 \qquad\text{ (B) }\ 17 \qquad\text{ (C) }\ 11 \qquad\text{ (D) }\ 19 \qquad\text{ (E) }\ 13$

We can find the value of $x$ and $y$ , and then plug everything into the last equation.

Using $x + z = 8$ , we have:

$x + 4 = 8$

$x = 8 - 4 = 4$

Using $x + y = 7$ , we have:

$4 + y = 7$

$y = 7 - 4 = 3$

Plugging the values into the last equation, we get:

$x + y + z = 4 + 3 + 4 = 7 + 4 = \boxed {\textbf {(C) } 11}$

~anabel.disher

Without finding the value of $x$ or $y$ , we can just plug $x + y$ and $z$ into the equation:

$x + y + z = 7 + 4 = \boxed {\textbf {(C) } 11}$

~anabel.disher