Step One
Change 2 1/16 into an improper fraction. An improper fraction has a numerator and a denominator; the denominator < the numerator.
[tex]2\dfrac{1}{16} =\dfrac{2*16 + 1}{16} =\dfrac{33}{16}[/tex]
Step Two
Set up the proportion.
2 1/16 cup : 2/5 product :: x cups peanuts / 1 cup product.
x = 2 1/16 cup / 2/5
Step 3
Solve for x.
[tex] x = \dfrac{\dfrac{33}{16}}{\dfrac{2}{5} } [/tex]
Invert and multiply the 2/5
[tex] x = \dfrac{33}{16} *\dfrac{5}{2}[/tex]
x = 165/32 = 5 5/32 <<<< Fraction Answer
which is an awkward result especially if you intend to make this peanut butter.
x = 5 5/32 = 5.15625 <<<< Decimal ansawer
Method two
Change all the fractions to decimals
2 1/16 = 2.0625
2/5 = 0.4
Set up the proportion.
2.0625/0.4 = x / 1
x = 2.0625/0.4 = 5.15625 cups of peanuts are needed.
One of these two answers should be what you are given as choices.
Answer: The number of ounces of peanuts that will make 1 jar of peanut butter is [tex]5\dfrac{5}{12}.[/tex]
Step-by-step explanation: Given that a bag with [tex]2\dfrac{1}{6}[/tex] ounces of peanuts can make [tex]\dfrac{2}{5}[/tex] of a jar of peanut butter.
We are to find the number of ounces of peanuts that will make one jar of peanut butter.
We will be using the UNITARY method to solve the problem.
We have
Number of ounces of peanuts that will make [tex]\dfrac{2}{5}[/tex] of a jar of peanut butter is
[tex]2\dfrac{1}{6}=\dfrac{13}{6}.[/tex]
So, number of ounces of peanuts that will make 1 jar of peanut butter will be
[tex]\dfrac{\frac{13}{6}}{\frac{2}{5}}=\dfrac{13}{6}\times\dfrac{5}{2}=\dfrac{65}{12}=5\dfrac{5}{12}.[/tex]
Thus, the number of ounces of peanuts that will make 1 jar of peanut butter is [tex]5\dfrac{5}{12}.[/tex]
