A backpacker is packing survival rations that consists of granola bars and packets of peanuts butter. A granola bar has 470 food calories and a packet of peanut butter has 90 food calories.The backpacker is packing survival rations using a total of 10 granola bars and packets of peanut butter combined , and the granola bars and packets of peanut butter have a total of 1,660 food calories. Which of the following systems of equations can be used to determine the number of granola bars g, and packets of peanut butter p, that are in the survival rations?

Options

A. `280(g+p)=1,660 `
`g-p=10`
B. `90g+470p=1,660`
`g-p=10`
C. `90g+470p=1,660`
`g=10-p`
D. `470g+90p=1,660`
`g=10-p`

Answer

To solve the problem, we need to set up a system of equations based on the information provided.

### Step 1: Define the variables
Let:
- \( g \) = number of granola bars
- \( p \) = number of packets of peanut butter

### Step 2: Set up the first equation
We know that the total number of granola bars and packets of peanut butter combined is 10. This can be expressed as:
\[ g + p = 10 \]

### Step 3: Set up the second equation
Next, we know the total food calories from the granola bars and peanut butter. Each granola bar has 470 calories and each packet of peanut butter has 90 calories. The total calories consumed is 1660. This can be expressed as:
\[ 470g + 90p = 1660 \]

### Step 4: Write the system of equations
Now we have a system of two equations:
1. \( g + p = 10 \)
2. \( 470g + 90p = 1660 \)

### Step 5: Solve the system of equations
From the first equation, we can express \( g \) in terms of \( p \):
\[ g = 10 - p \]

Now, substitute \( g \) in the second equation:
\[ 470(10 - p) + 90p = 1660 \]

Expanding this gives:
\[ 4700 - 470p + 90p = 1660 \]
Combining like terms:
\[ 4700 - 380p = 1660 \]

Now, isolate \( p \):
\[ -380p = 1660 - 4700 \]
\[ -380p = -3040 \]
\[ p = \frac{3040}{380} \]
\[ p = 8 \]

Now substitute \( p \) back into the equation for \( g \):
\[ g = 10 - p = 10 - 8 = 2 \]

### Final Answer
Thus, the backpacker is packing:
- \( g = 2 \) granola bars
- \( p = 8 \) packets of peanut butter