20% of the eggs at a stall are large, 25% of the remaining ones are medium and the rest are small. Small eggs cost 10 cents, Medium eggs cost 13 cents and large eggs cost 16 cents. If there are 800 eggs altogether, how much does the egg seller collect if he sells all the eggs?
First, we need to find out the number of large eggs at the stall. If 20% of the 800 eggs are large, there are:
0.2 x 800 = 160 large eggs
The remaining eggs are:
800 - 160 = 640
Out of the 640, 25% are medium, which means there are:
0.25 x 640 = 160 medium eggs
The rest are small eggs, which is:
640 - 160 = 480 small eggs
To find out how much the egg seller will collect, we need to multiply the number of each size of eggs by their respective prices and then add them up.
For large eggs:
160 x $0.16 = $25.60
For medium eggs:
160 x $0.13 = $20.80
For small eggs:
480 x $0.10 = $48.00
Therefore, the total amount the egg seller will collect if he sells all the eggs is:
$25.60 + $20.80 + $48.00 = $94.40
Let's calculate step by step:
Step 1: Calculate the number of large eggs
Given that 20% of the eggs are large and there are 800 eggs in total, we can calculate the number of large eggs:
Number of large eggs = 20% of 800 = (20/100) * 800 = 160 large eggs
Step 2: Calculate the number of remaining eggs
The remaining eggs would be 100% - 20% = 80% of the total eggs.
Number of remaining eggs = 80% of 800 = (80/100) * 800 = 640 eggs
Step 3: Calculate the number of medium eggs
Given that 25% of the remaining eggs are medium-sized, we can calculate the number of medium-sized eggs:
Number of medium eggs = 25% of 640 = (25/100) * 640 = 160 medium eggs
Step 4: Calculate the number of small eggs
The remaining eggs will be the small eggs, as mentioned in the question:
Number of small eggs = Remaining eggs = 640 eggs
Step 5: Calculate the total amount collected for each type of egg
The cost of small eggs is 10 cents per egg, so the total amount collected for the small eggs is:
Amount collected for small eggs = Number of small eggs * Cost per small egg = 640 * 10 cents = 6400 cents
The cost of medium eggs is 13 cents per egg, so the total amount collected for the medium eggs is:
Amount collected for medium eggs = Number of medium eggs * Cost per medium egg = 160 * 13 cents = 2080 cents
The cost of large eggs is 16 cents per egg, so the total amount collected for the large eggs is:
Amount collected for large eggs = Number of large eggs * Cost per large egg = 160 * 16 cents = 2560 cents
Step 6: Calculate the total amount collected for all eggs
The total amount collected for all eggs is the sum of the amounts collected for each type of egg:
Total amount collected = Amount collected for small eggs + Amount collected for medium eggs + Amount collected for large eggs
Total amount collected = 6400 cents + 2080 cents + 2560 cents = 11040 cents
Therefore, the egg seller collects 11040 cents if he sells all the eggs.