There are two basketball teams in a small town, the Miners and their opponents. In a particular game, the miners score twenty less than two times what their opponents score. A total of #127# points are scored. How many points do the miners score?

Let the number of points scored by the Miner's be #2x - 20# and that of their opponents be #x#. We can then state:

#(x) + (2x - 20) = 127#

#3x - 20 = 127#

#3x = 147#

#x = 49#

Hence, the opponents scored #49# points while the Miner's scored #78#. Quite a blowout!

Hopefully this helps!

Let's set up an equation.

Miners: #m#
Opponent: #x#

#m = 2x - 20#
#m + x = 127#

The first equation represents the number of points scored by the Miners with regards to the number of points scored by the opponent. The second equation shows the total amount of points scored is made up of the points scored by each team.

We've just created a system of equations. Let's solve for each variable and identify how many points were scored by the Miners.

First, plug in #2x-20# for #m# in the second equation.

#(2x-20) + x = 127#

Solve for #x#.

#3x - 20 = 127#

#3x = 147#

#x = 49#

We've determined that the opposing team (#x#) scored #49# out of the total #127# points scored. Now we must identify the amount of points the Miners scored.

Plug in #49# for #x# in the second equation, and solve for #m#.

#m + (49) = 127#

#m = 78#

The Miners scored #78# total points.