Gregg has made 40% of his free-throw shots, after attempting 20 shots at a free-throw competition. How many more consecutive shots must he make in order to increase his percentage to 50%?
he has made .4*20 = 8 of 20
he shoots total of 20 + x shots
8 + x = .5(20+x)
8 + x = 10 + .5 x
.5 x = 2
x = 4
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check
he has now shot 24
and has made 8+4 = 12
sure enough 12/24 = .5
thank you for answering the question but I don't understand how you got 10+5x?
To find out how many more consecutive shots Gregg must make in order to increase his percentage to 50%, we need to calculate the number of successful shots he needs to make and the total number of attempts.
First, let's determine how many successful free-throw shots Gregg has made so far:
40% of 20 shots = (40/100) * 20 = 8 successful shots
To increase his percentage to 50%, Gregg needs to make the total number of successful shots greater than or equal to 50% of the total number of attempts.
Let's denote the number of additional successful shots Gregg needs to make as 'x'.
The total number of successful shots after making 'x' more shots will be 8 + x.
The total number of attempts after making 'x' more shots will be 20 + x.
To increase his percentage to 50%:
(8 + x) / (20 + x) ≥ 50/100
Cross-multiply to solve for 'x':
(8 + x) * 100 ≥ (20 + x) * 50
800 + 100x ≥ 1000 + 50x
100x - 50x ≥ 1000 - 800
50x ≥ 200
x ≥ 200/50
x ≥ 4
Therefore, Gregg needs to make at least 4 more consecutive shots in order to increase his free-throw shooting percentage to 50%.
To find out how many more consecutive shots Gregg must make to increase his percentage to 50%, we need to set up an equation.
Let's begin by determining how many free throws Gregg has made so far. Since he has made 40% of his 20 attempts, we can calculate it as follows:
40% of 20 = 0.4 x 20 = 8 free throws made
Now, let's denote the number of consecutive shots Gregg needs to make as "x." Since he wants to increase his free-throw percentage to 50%, we can set up the equation:
(8 + x) / (20 + x) = 50/100
Simplifying this equation, we have:
(8 + x) / (20 + x) = 1/2
Now, we can cross multiply:
2(8 + x) = 20 + x
Expanding this equation, we get:
16 + 2x = 20 + x
Simplifying, we have:
2x - x = 20 - 16
x = 4
Therefore, Gregg needs to make 4 more consecutive shots to increase his free-throw percentage to 50%.