Two (2) Buckets were bought for X dollars each ($X) and a third bucket is bought for $less than twice the price of the first two buckets.

(a) Write down an expression for the total cost of the three buckets

(b) If the total cost of the buckets was less than $34. write an inequality in X and solve it.

(c) If x is a whole number, state the maximum cost of the buckets

2x-3(x-2)=$34

2x-3(x-2)=$34

(a) The cost of the first two buckets is 2X dollars each, so the total cost of the first two buckets is 2X + 2X = 4X dollars.

The third bucket is bought for less than twice the price of the first two buckets, which is less than 2(2X) = 4X dollars. Let's assume the cost of the third bucket is Y dollars.

So, the expression for the total cost of the three buckets is:
Total cost = Cost of first two buckets + Cost of the third bucket
Total cost = 4X + Y

(b) If the total cost of the buckets is less than $34, we can write the inequality as:
4X + Y < 34

(c) If X is a whole number, we need to find the maximum value of X that satisfies the inequality 4X + Y < 34.

Let's assume the cost of the third bucket is as low as possible, which is 0 dollars.

So, the inequality becomes:
4X + 0 < 34
4X < 34
X < 34/4
X < 8.5

Since X is a whole number, the maximum cost of the buckets would be when X is equal to 8.
Therefore, the maximum cost of the buckets would be 4X = 4(8) = 32 dollars.

(a) To find the expression for the total cost of the three buckets, let's first represent the cost of the first two buckets as X dollars each. Therefore, the total cost of the first two buckets would be 2X dollars, as there are two buckets bought for X dollars each.

Now, let's represent the cost of the third bucket as less than twice the price of the first two buckets. We can write this as 2X - Y dollars, where Y is the amount less than twice the price of the first two buckets.

Therefore, the expression for the total cost of the three buckets would be:
Total cost = Cost of the first two buckets + Cost of the third bucket = 2X + (2X - Y) = 4X - Y dollars.

(b) If the total cost of the buckets is less than $34, we can write an inequality using the expression derived in part (a):

4X - Y < 34

To solve this inequality, we need more information about the relationship between X and Y. Without additional information, we cannot solve it.

(c) If X is a whole number and we want to determine the maximum cost of the buckets, we need to find the largest possible value for X.

Since X represents the cost of each of the first two buckets, it must be a positive integer. However, without any additional constraints or a range for X, we cannot determine a maximum cost for the buckets.