Mitchell earned a total score of 55 points. Twenty percent of the baskets he made were worth three-points each. If four-fifths of the two-point baskets Mitchell attempted were successful and he made one-third of the three-point baskets he attempted, what is the total number of baskets that Mitchell attempted?

You don't mention his free throws made. If that number is zero, solve these equations:

x = number of 3-point shots made
y = number of 2-point shots made

3x + 2y = 55
x = 0.2(x+y)

5x = x+y
y = 4x
3x + 8x = 55
x = 5
y = 20

Total Shots attempted = 3x + (5/4) y
= 15 + 25 = 40

To find the total number of baskets that Mitchell attempted, we can break down the information given step by step.

Let's represent the total number of baskets attempted by 'x'.

First, we know that Mitchell made 20% of the baskets worth three points each. Therefore, the number of successful three-point baskets can be calculated as 20% of the total number of baskets attempted: 0.2x.

Next, we know that four-fifths of the two-point baskets Mitchell attempted were successful. So, the number of successful two-point baskets can be calculated as 4/5 or 0.8 times the total number of two-point baskets attempted: 0.8(x - 0.2x) = 0.8(0.8x) = 0.64x.

Additionally, we know that Mitchell made one-third of the three-point baskets he attempted. So, the total number of three-point baskets attempted can be calculated as three times the number of successful three-point baskets: 3(0.2x) = 0.6x.

Now, we can calculate the total number of baskets attempted by adding the three types of baskets: x + 0.64x + 0.6x = 2.24x.

Given that the total score earned by Mitchell was 55 points, we can set up the following equation:

(3 points per successful three-point basket)(0.2x) + (2 points per successful two-point basket)(0.64x) = 55

0.6x + 1.28x = 55
1.88x = 55
x = 55 / 1.88 ≈ 29.26

Since the total number of baskets attempted cannot be fractional, we can round up the value of x to the nearest whole number.

Therefore, Mitchell attempted approximately 30 baskets in total.