Mike asks Billy to help him run his lemonade stand. He’ll either pay him 2/5 of ½ of the stand’s profits, or 1/3 of ¾ of the stand’s profits. Which should Billy choose to maximize the amount he will earn, and by what amount will his earnings be increased?
2/5 * 1/2 = 1/5
1/3 * 3/4 = 1/4
1/4 is 25% more than 1/5
1/2
To determine which option Billy should choose to maximize his earnings, let's evaluate both scenarios.
1. Option 1: Billy will be paid 2/5 of 1/2 of the stand's profits.
- Multiply the fractions: 2/5 * 1/2 = 2/10 or 1/5.
- Billy will receive 1/5 of the stand's profits.
2. Option 2: Billy will be paid 1/3 of 3/4 of the stand's profits.
- Multiply the fractions: 1/3 * 3/4 = 3/12 or 1/4.
- Billy will receive 1/4 of the stand's profits.
Comparing the two options, Billy should choose Option 2, where he will receive 1/4 of the stand's profits. This option offers a higher fraction of the profits compared to Option 1 (1/4 > 1/5).
To calculate the increased amount that Billy will earn, we need to find the difference between the two scenarios:
1/4 (Option 2) - 1/5 (Option 1) = 5/20 - 4/20 = 1/20.
Therefore, by choosing Option 2, Billy will increase his earnings by 1/20 of the stand's profits.
To determine which option Billy should choose to maximize his earnings, we need to compare the two options and calculate the amounts for each.
Option 1: 2/5 of ½ of the stand's profits
To calculate this amount, we first need to find ½ of the stand's profits, and then calculate 2/5 of that amount.
Option 2: 1/3 of ¾ of the stand's profits
Similar to option 1, we need to find ¾ of the stand's profits, and then calculate 1/3 of that amount.
Let's calculate both options and compare the results:
Step 1: Finding ½ of the profits
To find ½ of the stand's profits, we divide the total profit by 2.
Step 2: Calculating 2/5 of ½ of the profits
To calculate 2/5 of ½ of the profits, we multiply 2/5 by the result obtained in step 1.
Step 3: Finding ¾ of the profits
To find ¾ of the stand's profits, we multiply the total profit by 3/4.
Step 4: Calculating 1/3 of ¾ of the profits
To calculate 1/3 of ¾ of the profits, we multiply 1/3 by the result obtained in step 3.
Now, compare the amounts obtained from both options and determine which one is greater. The option that yields the higher amount is the one that Billy should choose to maximize his earnings.