Pearson Algebra 1 Common Core, 2011
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Pearson Algebra 1 Common Core, 2011 View details
2. Solving Systems Using Substitution
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Exercise 39 Page 376

Make a table of values to organize the given information. Then, using the table create a system of equations.

2.75 seconds

Practice makes perfect

We can use the given information to create a system of equations.

  • Let x represent the number of seconds that have passed since Firework B was launched.
  • Let y represent the height the firework after x seconds.

    From here, we will make a table of values to organize the given information. Note that Firework A is launched 0.25 seconds after Firework B is launched, so to account for the number of seconds it has traveled, we have to subtract 0.25 from x.

    Firework A Firework B
    Verbal Expression Algebraic Expression Verbal Expression Algebraic Expression
    Number of seconds (s) x- 0.25 Number of seconds (s) x
    Speed (ft/s) 220 Speed (ft/s) 200
    Height (ft) 220( x- 0.25) Height (ft) 200 x
    Set the equation y= 220( x- 0.25) Set the equation y= 200 x
    Using this table, we can create the system as follows. y=220(x-0.25) & (I) y=200x & (II) The fireworks are set to explode at the same height, so to determine the time at which the firework explodes we must solve for x. To do this, we will use the Substitution Method and substitute the second equation into the first one.
    y=220(x-0.25) & (I) y=200x & (II)
    200x=220(x-0.25) y=200x
    200x=220x-55 y=200x
    - 20x=- 55 y=200x
    x=2.75 y=200x
    After 2.75 seconds the fireworks will explode at the same height.