Problem Solving On System Of Linear Equations, 1. One Angle Is Two Degrees More Than Its Complement. Find The Measures Of The Two Complementary Angles

Problem solving on System of Linear Equations

1. One angle is two degrees more than its complement. Find the measures of the two complementary angles.

2. JM is twelve years older than his brother PJ. Four years from now, PJ will be two-thirds as old as JM will be four years from now. How old are they now?

3. Rey has two investments that earn an annual income of Php49,800. One investment yields 7% interest and the other 8%. How much is invested at each rate if the total amount invested is Php640,000.

 

Answer:

1. 44 and 46

2. PJ is 20, JM is 32

3. Investment with 7% interest = 140,000 ;

   Investment with 8% interest = 500,000

Step-by-step explanation:

1. x = 1st angle

  x +2 = 2nd angle

  Completentary angles are equal to 90 degrees

  x + (x + 2) = 90

   2x + 2 = 90

   2x = 90 - 2

   2x = 88

    x = 44

    (44) + 2 = 46

2. Let x = Age of PJ

         x + 12 = Age of JM

         2/3(x + 12 + 4) = x + 4

         2/3(x + 16) = x + 4

         (2x+32)/3 = x + 4

         2x + 32 = 3x + 12

         32 - 12 = 3x - 2x

         20 = x

         (20) + 12 = 32

3. 1st investment = x

   2nd investment = y

  0.07x + 0.08y = 49,800

         x  + y = 640,000

 

  0.07x + 0.08y = 49,800

  -0.07(x + y = 640,000)

  0.07x + 0.08y = 49,800

 -0.07x - 0.07y = -44,800

                0.01y = 5,000

                       y = 500,000

   x + (500,000) = 640,000

   x = 640,000 - 500,000

   x = 140,000

You can check if you have doubts :)