Question

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 1

To determine how many smaller boxes equal the same amount of cereal in the larger box, the equations 12 + 7.6n equals 6 + 8n are set equal to each other and solved. After simplifying, the solution is found to be n = 15, meaning 15 smaller boxes contain the same amount of cereal as the larger box.

Step-by-step explanation:

The question asks us to find the number of smaller boxes that contain the same amount of cereal as one larger box given two different expressions that represent the amount of cereal. The equations provided are 12 + 7.6n and 6 + 8n, where n represents the number of smaller boxes. To find the value of n that makes these two expressions equal, we need to solve the equation 12 + 7.6n = 6 + 8n.

1. Subtract 6 from both sides of the equation to get 6 + 7.6n = 8n.
2. Subtract 7.6n from both sides to get 6 = 0.4n.
3. Divide both sides by 0.4 to get n = 15.

Therefore, 15 smaller boxes of cereal are equivalent to the amount of cereal in one larger box according to the given expressions.

Answer 2

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

`12+7.6n= 6+ 8n`

Solve for n

`8n-7.6n=12-6`

`0.4n=6`

`n=15`

so

The amount of cereal in a large box is

`6+ 8n=6+8(15)=6+120=126\ ounces`

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

`(126)/(12)= 10.5`

therefore

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