Olivia is making granola bars. She will use 17.9 ounces of pistachios, 12.6 ounces of almonds, 12.5 ounces of walnuts, and 12.5 ounces of cashews. This amount will make 25 bars. How many ounces of nuts are in each granola bar?

Proportional Comparisons / Directly proportional are comparisons of two or more numbers where one number increases, the other numbers also increase at the same rate

Can be formulated

[tex]\displaystyle \frac {x1} {y1} = \frac {x2} {y2}[/tex]

so that if:

x = 2

then

[tex]\displaystyle y ={ \frac {y} {x} \times \: 2}[/tex]

While the reversal value comparison / inversely proportional is the comparison of two or more numbers where one number increases, the other number decreases in value

or when one value decreases at the same rate that the other increases

Can be formulated

[tex]\displaystyle \frac {x1} {y2} = \frac {x2} {y1}[/tex]

so that if:

x = 2

then

[tex]\displaystyle y = \frac {x} {y} \times \: 2[/tex]

Known

Olivia is making 25 granola bars with 17.9 ounces of pistachios, 12.6 ounces of almonds, 12.5 ounces of walnuts, and 12.5 ounces of cashews.

Asked

ounces of nuts are in each granola bar

Answer

We add all the nuts together in 25 bars :

= 17.9+12.6+12.5+12.5

[tex]\large{\boxed{= 55.5\:nuts}}[/tex]

Because this includes Proportional Comparisons / Directly proportional, the equation becomes:

[tex]\displaystyle \frac{1~bar}{25~bars}=\frac{x\:nuts}{55.5~nuts}[/tex]

[tex]\displaystyle x\:nuts=\frac{55.5\times1}{25}[/tex]

[tex]\displaystyle x=\large{\boxed{\bold{2.22\:nuts}}}[/tex]

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Keywords: bars, nuts, Proportional Comparisons / Directly proportional