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QuestionHow much blood is needed for 3 tests if each requires 2142 \frac{1}{4} cc? A. 31123 \frac{1}{12} cc B. 6146 \frac{1}{4} cc C. 6126 \frac{1}{2} cc D. 6346 \frac{3}{4} cc E. 7127 \frac{1}{2} cc

Studdy Solution

STEP 1

Assumptions1. Each test requires 14 \frac{1}{4} cubic centimeters of blood. The lab runs three different tests3. The total amount of blood required is the sum of the blood required for each test

STEP 2

First, we need to convert the mixed number 2142 \frac{1}{4} to an improper fraction. The formula to convert a mixed number to an improper fraction isImproper fraction=(whole number×denominator)+numerator\text{Improper fraction} = (\text{whole number} \times \text{denominator}) + \text{numerator}

STEP 3

Now, plug in the given values for the whole number, denominator, and numerator to calculate the improper fraction.
Improper fraction=(2×)+1\text{Improper fraction} = (2 \times) +1

STEP 4

Calculate the improper fraction.
Improper fraction=(2×4)+1=9\text{Improper fraction} = (2 \times4) +1 =9So, 2142 \frac{1}{4} is equivalent to 94\frac{9}{4}.

STEP 5

Now that we have the amount of blood required for one test, we can find the total amount of blood required for three tests. This can be done by multiplying the amount of blood required for one test by the number of tests.
Total blood required=Amount of blood for one test×Number of tests\text{Total blood required} = \text{Amount of blood for one test} \times \text{Number of tests}

STEP 6

Plug in the values for the amount of blood for one test and the number of tests to calculate the total blood required.
Total blood required=94×3\text{Total blood required} = \frac{9}{4} \times3

STEP 7

Calculate the total blood required.
Total blood required=94×3=274\text{Total blood required} = \frac{9}{4} \times3 = \frac{27}{4}

STEP 8

Finally, we convert the improper fraction back to a mixed number to get the final answer. The formula to convert an improper fraction to a mixed number isMixed number=Whole number+umeratorDenominator\text{Mixed number} = \text{Whole number} + \frac{\text{umerator}}{\text{Denominator}}where the whole number is the quotient of the numerator divided by the denominator, and the numerator is the remainder of the numerator divided by the denominator.

STEP 9

Calculate the whole number and the numerator.
Whole number = 274=6\frac{27}{4} =6 (quotient)
umerator = 27mod  4=327 \mod4 =3 (remainder)

STEP 10

Plug in the values for the whole number and the numerator to calculate the mixed number.
Mixed number=6+34\text{Mixed number} =6 + \frac{3}{4}So, the minimum amount of blood needed is 6346 \frac{3}{4} cubic centimeters. The correct answer is () 6346 \frac{3}{4} cubic centimeters.

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