qTwo (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) The expression for the total cost of the three buckets can be written as:
Total Cost = Cost of the first bucket + Cost of the second bucket + Cost of the third bucket
Let's assume that the cost of the first two buckets is X dollars each. Therefore, the cost of the first bucket is X dollars and the cost of the second bucket is also X dollars.
The cost of the third bucket is less than twice the price of the first two buckets, which means it is less than 2X dollars.
Therefore, the expression for the total cost of the three buckets would be:
Total Cost = X + X + (less than 2X)
(b) If the total cost of the buckets is less than $34, we can write the inequality as:
Total Cost < $34
Substituting the expression for the total cost from part (a), we get:
X + X + (less than 2X) < $34
Simplifying the inequality, we have:
2X + (less than 2X) < $34
Since the third bucket costs less than 2X, we can denote it as Y dollars, where Y < 2X. Now, we can rewrite the inequality as:
2X + Y < $34
(c) If X is a whole number, the maximum cost of the buckets would be when X is maximized. Given that the total cost of the three buckets should be less than $34, let's find the maximum value of X.
Since we don't have a specific value for Y, let's assume Y = 0 (the minimum value).
Now, we can rewrite the inequality from part (b) as:
2X + 0 < $34
Simplifying the inequality, we have:
2X < $34
Dividing both sides of the inequality by 2, we get:
X < $17
Thus, the maximum cost of the buckets would be $17 when X is a whole number.