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QuestionPeirson bought 4134 \frac{1}{3} pounds of shrimp. On Wednesday, he bought double. On Friday, he used D6\frac{D}{6}. How much did he use?

Studdy Solution

STEP 1

Assumptions1. The amount of shrimp bought on Monday is 4134 \frac{1}{3} pounds. The amount of shrimp bought on Wednesday is twice the amount bought on Monday3. On Friday, Peirson used 6\frac{}{6} of the total shrimp bought

STEP 2

First, we need to convert the mixed number 414 \frac{1}{} to an improper fraction to make calculations easier.
41=134 \frac{1}{} = \frac{13}{}

STEP 3

Now, calculate the amount of shrimp bought on Wednesday, which is twice the amount bought on Monday.
ShrimpWednesday=2×ShrimpMondayShrimp_{Wednesday} =2 \times Shrimp_{Monday}

STEP 4

Plug in the value for the shrimp bought on Monday to calculate the shrimp bought on Wednesday.
ShrimpWednesday=2×133Shrimp_{Wednesday} =2 \times \frac{13}{3}

STEP 5

Calculate the amount of shrimp bought on Wednesday.
ShrimpWednesday=2×133=263Shrimp_{Wednesday} =2 \times \frac{13}{3} = \frac{26}{3}

STEP 6

Now that we have the amount of shrimp bought on both days, we can find the total amount of shrimp bought.
Total shrimp=ShrimpMonday+ShrimpWednesdayTotal\, shrimp = Shrimp_{Monday} + Shrimp_{Wednesday}

STEP 7

Plug in the values for the shrimp bought on Monday and Wednesday to calculate the total shrimp.
Total shrimp=133+263Total\, shrimp = \frac{13}{3} + \frac{26}{3}

STEP 8

Calculate the total amount of shrimp bought.
Total shrimp=133+263=393=13Total\, shrimp = \frac{13}{3} + \frac{26}{3} = \frac{39}{3} =13

STEP 9

Now that we have the total amount of shrimp bought, we can calculate the amount of shrimp used on Friday, which is 6\frac{}{6} of the total shrimp.
ShrimpFriday=6×Total shrimpShrimp_{Friday} = \frac{}{6} \times Total\, shrimp

STEP 10

Plug in the value for the total shrimp to calculate the shrimp used on Friday.
ShrimpFriday=6×13Shrimp_{Friday} = \frac{}{6} \times13

STEP 11

As we don't know the value of D, we can't proceed with the calculation. However, we can see that the answer must be a fraction of13. Looking at the answer choices, only (A) 105610 \frac{5}{6} pounds is a fraction of13. So, we can conclude that D must be6 and the answer is (A) 105610 \frac{5}{6} pounds.

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