Question

Hunter needs 10 oz of a snack mix that is made up of seeds and dried fruit. The seeds cost $1.50 per ounce and the dried fruit costs $2.50 per ounce. The 10 oz snack mix costs $2.20 per ounce.

Let x = the amount of seeds.

Let y = the amount of dried fruit.


How much of each snack should Hunter purchase to satisfy the scenario?

Enter your answers in the boxes.

Answer 1

To solve for the amounts of seeds (\(x\)) and dried fruit (\(y\)) that Hunter should purchase, we can set up a system of equations based on the given information.

### Given:
1. Total weight of the mix:
\(x + y = 10\) (1)

2. Total cost of the mix:
The total cost of the snack mix can be calculated as the cost per ounce multiplied by the total weight. Since the mix costs $2.20 per ounce, for 10 ounces, the total cost is:
\(2.20 \times 10 = 22\) dollars.

The cost equation based on the amounts of seeds and dried fruit:
\(1.50x + 2.50y = 22\) (2)

### Now we can solve these equations:

From equation (1):
\[
y = 10 - x \tag{3}
\]

Substituting (3) into equation (2):
\[
1.50x + 2.50(10 - x) = 22
\]
\[
1.50x + 25 - 2.50x = 22
\]
\[
-1.00x + 25 = 22
\]
\[
-1.00x = 22 - 25
\]
\[
-1.00x = -3
\]
\[
x = 3
\]

Now substituting \(x\) back into equation (3) to find \(y\):
\[
y = 10 - 3
\]
\[
y = 7
\]

### Conclusion:
Hunter should purchase:
- **3 oz of seeds**
- **7 oz of dried fruit**

You can enter these values in the boxes:
- Seeds: **3**
- Dried Fruit: **7**