1999 CEMC Pascal Problems/Problem 7

Problem

If $2x - 1 = 5$ and $3y + 2 = 17$ , then the value of $2x + 3y$ is

$\text{ (A) }\ 8 \qquad\text{ (B) }\ 19 \qquad\text{ (C) }\ 21 \qquad\text{ (D) }\ 23 \qquad\text{ (E) }\ 25$

Solution 1

Solving the equations for $x$ and $y$ , we get:

$2x - 1 = 5$

$2x = 6$

$x = 3$

$3y + 2 = 17$

$3y = 15$

$y = 5$

Plugging this into the expression, we get:

$2x + 3y = 2 \times 3 + 3 \times 5$

$=6 + 15$

$=21$

~anabel.disher

Solution 2

We can notice that the first equation contains $2x$ and the second equation contains $3y$ , like in the expression. This means that we can simply add the equations, and solve for $2x + 3y$ :

$2x - 1 + 3y + 2 = 5 + 17$

$2x + 3y + 1 = 22$

$2x + 3y = 21$

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1999 CEMC Pascal Problems/Problem 7

Problem

Solution 1

Solution 2