A quarterback completes 18 of 33 passes during the first three quarters of a football game. He completes every pass in the fourth quarter and 62.5% of his passes for the entire game. How many passes does the quarterback throw in the fourth quarter?
(Would help if it is in a proportion!
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To figure out how many passes the quarterback throws in the fourth quarter, we can use a proportion.
Let's assume that the quarterback throws "x" passes in the fourth quarter.
We can set up the proportion using the completion percentages:
(18 + x) / (33 + x) = 62.5% / 100%
To solve this proportion, we can cross-multiply:
(18 + x) * 100% = (33 + x) * 62.5%
Simplifying this equation:
(18 + x) = (33 + x) * 0.625
Expanding the equation:
18 + x = 20.625 + 0.625x
Now, we can isolate the "x" variable:
x - 0.625x = 20.625 - 18
Simplifying:
0.375x = 2.625
Finally, solving for x:
x = 2.625 / 0.375
x ≈ 7
Therefore, the quarterback throws approximately 7 passes in the fourth quarter.
To find the number of passes the quarterback throws in the fourth quarter, we can set up a proportion using the completion percentage for the entire game.
Let's say "x" represents the number of passes attempted in the fourth quarter. The proportion can be set up as follows:
18 + x (completed passes in first three quarters + completed passes in fourth quarter) / (33 + x) (total passes attempted in first three quarters + total passes attempted in fourth quarter) = 62.5%
To solve for "x", we can cross-multiply and solve the equation:
(18 + x) / (33 + x) = 62.5%
62.5% is equivalent to the decimal 0.625. Therefore,
(18 + x) / (33 + x) = 0.625
Next, we can cross-multiply:
0.625 * (33 + x) = 18 + x
20.625 + 0.625x = 18 + x
0.625x - x = 18 - 20.625
-0.375x = -2.625
x = (-2.625) / (-0.375)
x = 7
Therefore, the quarterback throws 7 passes in the fourth quarter.