Question

Apple needs 12 ounces of a stir fry mix that is made up of rice and dehydrated veggies. The rice cost $1.73 per ounce and the veggies costs $3.38 per ounce. Apple has $28 to spend and plans to spend it all.

Let x = amount of rice
Let y = the amount of veggies

Part 1: Create a system of equations to represent the scenario.

Part 2: Solve your system using any method. Write your answer as an ordered pair.

Part 3: Interpret what your answer means (how much rice and how much veggies apple buys)

Answer 1

Part 1:
The total amount of the stir fry mix is 12 ounces, so we have:

x + y = 12 (equation 1)

The total cost of the mix is $28, so we have:

1.73x + 3.38y = 28 (equation 2)

Part 2:
We can solve the system of equations in a few ways. Here, we will use the substitution method.

From equation 1, we have:

y = 12 - x

Substituting this into equation 2, we get:

1.73x + 3.38(12 - x) = 28

Simplifying and solving for x, we get:

1.73x + 40.56 - 3.38x = 28
-1.65x = -12.56
x ≈ 7.62

So Apple needs approximately 7.62 ounces of rice. To find the amount of veggies, we can use equation 1:

y = 12 - x
y = 12 - 7.62
y ≈ 4.38

So Apple needs approximately 4.38 ounces of dehydrated veggies.

Part 3:
The solution to the system of equations is (7.62, 4.38), which means that Apple needs to buy approximately 7.62 ounces of rice and 4.38 ounces of dehydrated veggies to make the 12-ounce stir fry mix.

Answer 2

1. x + y = 12; 1.73x +3.38y = 28
2. (7.61, 4.39)
3. Apple needs to buy 7.61 ounces of rice and 4.39 ounces of veggies.

Explanation:

You want a system of equations, their solution, and the interpretation of the solution for the scenario that Apple will be buying 12 ounces total of rice (x) at $1.73 per ounce and veggies (y) at $3.38 per ounce.

1. Equations

The given relations can be expressed in two equations:

• x + y = 12 . . . . . . total ounces purchased
• 1.73x +3.38y = 28 . . . . . . total cost

2. Solution

The solution to these equations is shown in the attached graph. It is ...

(x, y) ≈ (7.61, 4.39)

3. Interpretation

For Apple to buy 12 ounces of ingredients at a total cost of $28, Apple needs to buy 7.61 ounces of rice and 4.39 ounces of veggies.

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Additional comment

If you understand the definitions of the variables, the interpretation is pretty straightforward:

x = ounces of rice to purchase: x = 7.61 means Apple needs to purchase 7.61 ounces of rice.

y = ounces of veggies to purchase: y = 4.39 means Apple needs to purchase 4.39 ounces of veggies.

My graphing calculator offers at least 3 different ways to solve a system of equations like this. I like the graphical solution, because it is convenient to type the equations in their original form, and the solution is given as an ordered pair.