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A cereal box manufacturer changes the size
of the box to increase the amount of cereal it
contains. The equations 12 + 7.6n and 6 + 8n,
where n is the number of smaller boxes, are
both representative of the amount of cereal that
the new larger box contains. How many smaller
boxes equal the same amount of cereal in the
larger box?

Answer :

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Answer:

10.5 small boxes equals the same amount of cereal in a large box

Step-by-step explanation:

see the attached figure to better understand the problem

Let

n is the number of smaller boxes

we know that

The equations

12 + 7.6n and 6 + 8n

are  both representative of the amount of cereal that  the new larger box  contains

so

[tex]12+7.6n= 6+ 8n[/tex]

Solve for n

[tex]8n-7.6n=12-6[/tex]

[tex]0.4n=6[/tex]

[tex]n=15[/tex]

so

The amount of cereal in a large box is

[tex]6+ 8n=6+8(15)=6+120=126\ ounces[/tex]

Remember that the amount of cereal in the smaller box is 12 ounces (see the attached figure)

so

Divide the volume of the larger box by the volume of the smaller box

[tex]\frac{126}{12}= 10.5[/tex]

therefore

10.5 small boxes equals the same amount of cereal in a large box

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