1. Chapter 4-5 Problem Solving: 3 by 3 Systems Objective: Using 3 x 3 systems

2. Example 1: There are 3 machines, A,B and C in a factory. 1) When all 3 work, they produce 287 bolts per hour. 2) When only A and C work, they produce 197 bolts per hour. 3) When A and B work, they produce 202 bolts per hour. How many bolts per hour can each machine produce alone? Translate: 1) A + B + C = 287 2) A+ C = 197 3) A + B = 202 Solve 2) for C= and 3) for B= Then substitute both into 1) to solve for A You should get: (112,90,85)

3. Example 2: In triangle PQR, 1) the measure of angle Q is 3 times the measure of angle P. 2) The measure of angle R is 20 degrees greater than the measure of angle P. Find all 3 angles. Where is the third equation? What prior knowledge do you need here? 3) The sum of the angles of a triangle add up to 180 Translate: 1) Q = 3P 2) R = P+60 3) P + Q + R = 180 Substitute both 1) and 2) into 3) for Q and R then solve for P. Use P to find the other 2 angles You should get: (24,72,84)