A field goal kicker has made 21 out of 30
attempted field goals so far this season. His
field goal average is 0.7.
How many consecutive field goals must he
make to increase his average to 0.8125?
let the number of consecutive extra attempts be x
then (21+x)/(30+x) = .8125 = 13/16
336 + 16x = 390 + 13x
solve for x
To solve this problem, we can use the following equation:
(21 + x) / (30 + x) = 0.8125
Let's solve for x:
Multiply both sides of the equation by (30 + x):
(21 + x) = 0.8125 * (30 + x)
Distribute 0.8125:
21 + x = 24.375 + 0.8125 * x
Subtract 0.8125 * x from both sides:
21 + x - 0.8125 * x = 24.375
Combine like terms:
0.1875 * x + 21 = 24.375
Subtract 21 from both sides:
0.1875 * x = 24.375 - 21
0.1875 * x = 3.375
Divide both sides by 0.1875:
x = 3.375 / 0.1875
x ≈ 18
Therefore, the kicker needs to make 18 consecutive field goals to increase his average to 0.8125.
To determine how many consecutive field goals the kicker must make to increase his average to 0.8125, we can use the formula for average:
Average = Total Made / Total Attempted
We know that his current field goal average is 0.7 and he has made 21 out of 30 attempted field goals. Let's represent the number of consecutive field goals he needs to make as 'x'. So, the updated formula will be:
0.8125 = (21 + x) / (30 + x)
To solve for 'x', we can cross-multiply and then solve the resulting equation. Here's how:
0.8125 * (30 + x) = 21 + x
24.375 + 0.8125x = 21 + x
0.8125x - x = 21 - 24.375
-0.1875x = -3.375
x = (-3.375) / (-0.1875)
x ≈ 18
Therefore, the kicker must make approximately 18 consecutive field goals to increase his average to 0.8125.