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Diego is thinking of two positive numbers. He says, “If we triple the first number and double the second number, the sum is 34.”
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Anonymous
0


  1. Write an equation that represents this clue. Then, find two possible pairs of numbers Diego could be thinking of.
  2. Diego then says, “If we take half of the first number and double the second, the sum is 14. Write an equation that could represent this description.
  3. What are Diego’s two numbers? Explain or show how you know. A coordinate plane is given here, in case helpful.


Sangeetha Pulapaka
0

Consider the first number to be variable x, and the second number to be variable y.


  1. The equation to represent this will be 3x + 2y = 34. The two possible pairs of numbers Diego could be thinking of is, (10, 2) and (8, 5).
  2. The equation to represent this will be \frac{1}{2}x + 2y = 14.
  3. We can solve these equations to find the two numbers. We can solve them algebraically or graphically.


           3x + 2y = 34

          \mp \frac{1}{2}x \mp 2x = \mp 14

         ------------------------------------

          3x -\frac{1}{2}x = 20

          \Rightarrow\frac{5x}{2} = 20

           \Rightarrow x = 8


Plugging in the value of x in 3x + 2y = 34, we solve for y, to get,

\Rightarrow2y = 34 - 3x

\Rightarrow 2y = 34 - 24 = 10

\Rightarrow y = 5


So, 8 and 5 are the two numbers. We can also use technology to plot the graph of these system of equations as shown below.