Question

solve for x and y to advance in the scavenger hunt, find the value of 2x - y

Explanation:

Step1: Set up proportion for x

Since the triangles are similar, corresponding sides are proportional: $\frac{2}{2+5} = \frac{3}{x}$

Step2: Solve for x

Cross-multiply: $2x = 3 \times 7$
$2x = 21$
$x = \frac{21}{2} = 10.5$

Step3: Set up proportion for y

Use similarity for the largest triangle: $\frac{2}{2+5+y} = \frac{3}{6}$

Step4: Solve for y

Cross-multiply: $2 \times 6 = 3 \times (7+y)$
$12 = 21 + 3y$
$3y = 12 - 21 = -9$
$y = -3$

Step5: Calculate 2x - y

Substitute x and y: $2(10.5) - (-3)$

Answer:

$2(10.5) - (-3) = 21 + 3 = 24$