Twenty-seven members of a West Virginia diet club celebrated the combined loss of 500 pounds by devouring a very large salad. The salad took two hours to prepare and four hours to eat. In fact, the salad was mixed in a swimming pool and included 890 individual vegetable. There were six times as many carrots as heads of lettuce and there were ten more cucumbers than heads of lettuce.
If a head of lettuce weighs two pounds, a carrot weighs four ounces, and a cucumber weighs one pound, how much did the total salad weigh?
L = heads of lettuce
r = carrots
u = cucumbers
L + r + u = 890 ... r = 6L ... u = L + 10
substituting ... L + 6L + L + 10 = 890
solve for L , substitute back for r and u
plug in the individual weights to find the total weight
To find the total weight of the salad, we need to determine the weight of each vegetable and then add them together.
Let's start by finding the number of heads of lettuce. We know that the weight of a head of lettuce is two pounds, and we need to find out how many heads of lettuce there are. Let's call the number of heads of lettuce "x." Therefore, the weight of the lettuce is 2x pounds.
Next, we are given that there were six times as many carrots as heads of lettuce. So, the number of carrots is 6x. We also know that the weight of a carrot is four ounces or 0.25 pounds. Therefore, the weight of the carrots is 0.25 * 6x = 1.5x pounds.
Finally, we are told that there were ten more cucumbers than heads of lettuce. So, the number of cucumbers is x + 10. We also know that the weight of a cucumber is one pound. Therefore, the weight of the cucumbers is 1 * (x + 10) = x + 10 pounds.
Now, we can determine the total weight of the salad by adding the weight of the lettuce, carrots, and cucumbers together:
Total weight = weight of lettuce + weight of carrots + weight of cucumbers
= 2x + 1.5x + (x + 10)
= 2x + 1.5x + x + 10
= 4.5x + 10
To find the value of "x" and the total weight of the salad, we need another piece of information.