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
(a) To find the total cost of the three buckets, we need to add up the cost of each bucket.
Let's call the cost of the first two buckets X, which means each bucket costs X dollars. The total cost of the first two buckets would be 2X.
Now, the cost of the third bucket is less than twice the price of the first two buckets. Let's represent this cost as 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 = 2X + Y
(b) If the total cost of the buckets is less than $34, we can write the following inequality:
2X + Y < 34
To solve this inequality, we need to isolate X to one side:
2X < 34 - Y
Divide both sides by 2:
X < (34 - Y) / 2
This inequality provides the upper limit for the possible values of X.
(c) If X is a whole number, we need to determine the maximum cost of the buckets.
Since the total cost of the buckets depends on X and Y, we need to consider the highest possible value for Y.
In this case, Y can be any value less than twice the price of the first two buckets. Let's say Y = 2X - 1 (one less than twice the price of the first two buckets).
So, the maximum cost of the buckets can be determined by substituting Y = 2X - 1 into the expression for the total cost:
Total cost = 2X + (2X - 1) = 4X - 1
To find the maximum cost, we need to maximize the value of X. Since X is a whole number, the maximum value of X would be the largest whole number that satisfies the inequality in part (b) (i.e., X < (34 - Y) / 2). By substituting the appropriate values for X and Y, we can find the maximum cost of the buckets.