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John and Gemma played a new computer game called Benga - Junior Cycle Mathematics - Question c - 2012

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John and Gemma played a new computer game called Benga. John scored two benga minus three penalties. His total score was seven points. He made the equation $2x - 3y ... show full transcript

Worked Solution & Example Answer:John and Gemma played a new computer game called Benga - Junior Cycle Mathematics - Question c - 2012

Step 1

Make an equation to represent Gemma’s score.

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Answer

Let the points for a benga be represented as xx and the points for a penalty as yy. Gemma's score can be modeled by the equation:
5x−5y=205x - 5y = 20

Step 2

Use simultaneous equations to find the number of points for a benga and the number of points for a penalty.

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Answer

We have two equations:

  1. 2x−3y=72x - 3y = 7
  2. 5x−5y=205x - 5y = 20

From the second equation, we can simplify it: x−y=4x - y = 4

Now, we can substitute yy from the first equation: y = rac{2}{3}x - rac{7}{3}

Substituting into the simplified equation:
x - rac{2}{3}x + rac{7}{3} = 4

Solving for xx, we have:

ightarrow x = 5$$ Substituting $x = 5$ back into one of the equations to find $y$: $$y = rac{1}{5}$$

Step 3

Verify your solutions in both equations.

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Answer

Substituting x=5x = 5 and y=1y = 1 into both equations:

  1. For John:
    2(5)−3(1)=72(5) - 3(1) = 7
    which simplifies to 7=77 = 7.
  2. For Gemma:
    5(5)−5(1)=205(5) - 5(1) = 20
    which simplifies to 20=2020 = 20.
    Both equations are satisfied, confirming the solutions are correct.

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