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Answer :
To determine which box gives you more cereal for your money, we'll compare the cost per cubic inch of cereal for both boxes. Here's the step-by-step procedure to solve this problem:
### Step 1: Calculate the volume of each box
First, we need to determine the volume of each cereal box in cubic inches.
Box 1 Dimensions: 16 in x 2 in x 4 in
Volume of Box 1 = Length x Width x Height
[tex]\[ \text{Volume of Box 1} = 16 \, \text{in} \times 2 \, \text{in} \times 4 \, \text{in} = 128 \, \text{cubic inches} \][/tex]
Box 2 Dimensions: 10 in x 8 in x 10 in
Volume of Box 2 = Length x Width x Height
[tex]\[ \text{Volume of Box 2} = 10 \, \text{in} \times 8 \, \text{in} \times 10 \, \text{in} = 800 \, \text{cubic inches} \][/tex]
### Step 2: Calculate the cost per cubic inch for each box
Next, we need to determine the cost per cubic inch of cereal for each box by dividing the price of the box by its volume.
Box 1 Price: [tex]$6.00
Cost per cubic inch for Box 1 = Price / Volume
\[ \text{Cost per cubic inch for Box 1} = \frac{6.00 \, \text{dollars}}{128 \, \text{cubic inches}} \approx 0.046875 \, \text{dollars per cubic inch} \]
Box 2 Price: $[/tex]2.00
Cost per cubic inch for Box 2 = Price / Volume
[tex]\[ \text{Cost per cubic inch for Box 2} = \frac{2.00 \, \text{dollars}}{800 \, \text{cubic inches}} = 0.0025 \, \text{dollars per cubic inch} \][/tex]
### Step 3: Compare the cost per cubic inch
Now, we compare the cost per cubic inch of each box to determine which one gives you more cereal for your money.
- Cost per cubic inch for Box 1: [tex]$0.046875
- Cost per cubic inch for Box 2: $[/tex]0.0025
### Conclusion:
Since the cost per cubic inch for Box 2 ([tex]$0.0025) is less than the cost per cubic inch for Box 1 ($[/tex]0.046875), Box 2 gives you more cereal for your money. Thus, Box 2 is the better deal.
### Step 1: Calculate the volume of each box
First, we need to determine the volume of each cereal box in cubic inches.
Box 1 Dimensions: 16 in x 2 in x 4 in
Volume of Box 1 = Length x Width x Height
[tex]\[ \text{Volume of Box 1} = 16 \, \text{in} \times 2 \, \text{in} \times 4 \, \text{in} = 128 \, \text{cubic inches} \][/tex]
Box 2 Dimensions: 10 in x 8 in x 10 in
Volume of Box 2 = Length x Width x Height
[tex]\[ \text{Volume of Box 2} = 10 \, \text{in} \times 8 \, \text{in} \times 10 \, \text{in} = 800 \, \text{cubic inches} \][/tex]
### Step 2: Calculate the cost per cubic inch for each box
Next, we need to determine the cost per cubic inch of cereal for each box by dividing the price of the box by its volume.
Box 1 Price: [tex]$6.00
Cost per cubic inch for Box 1 = Price / Volume
\[ \text{Cost per cubic inch for Box 1} = \frac{6.00 \, \text{dollars}}{128 \, \text{cubic inches}} \approx 0.046875 \, \text{dollars per cubic inch} \]
Box 2 Price: $[/tex]2.00
Cost per cubic inch for Box 2 = Price / Volume
[tex]\[ \text{Cost per cubic inch for Box 2} = \frac{2.00 \, \text{dollars}}{800 \, \text{cubic inches}} = 0.0025 \, \text{dollars per cubic inch} \][/tex]
### Step 3: Compare the cost per cubic inch
Now, we compare the cost per cubic inch of each box to determine which one gives you more cereal for your money.
- Cost per cubic inch for Box 1: [tex]$0.046875
- Cost per cubic inch for Box 2: $[/tex]0.0025
### Conclusion:
Since the cost per cubic inch for Box 2 ([tex]$0.0025) is less than the cost per cubic inch for Box 1 ($[/tex]0.046875), Box 2 gives you more cereal for your money. Thus, Box 2 is the better deal.
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