Mathematics, 13.07.2019 20:00 leo4687

You're a manager in a company that produces rocket ships. machine a and machine b both produce cockpits and propulsion systems. machine a and machine b produce cockpits at the same rate, and they produce propulsion systems at the same rate. machine a ran for 26 hours and produced 4 cockpits and 6 propulsion systems. machine b ran for 56 hours and produced 8 cockpits and 12 propulsion systems. we use a system of linear equations in two variables. can we solve for a unique amount of time that it takes each machine to produce a cockpit and to produce a propulsion system?

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Answer from: FlowerChild1229

No you cannot.

Step-by-step explanation:

Let c be the amount of time it takes each machine to make 1 cockpit, and p be the amount of time it takes each machine to make 1 propulsion system.

For Machine A, we have 4 cockpits; this would take 4c time. We also have 6 propulsion systems; this would take 6p time. Together it takes 26 hours; this would give us

4c+6p=26.

For Machine B, we have 8 cockpits; this would take 8c time. We also have 12 propulsion systems; this would take 12p time. Together it takes 56 hours; this would give us

8c+12p=56

This gives us the system

$\left \{ {{4c+6p=26} \atop {8c+12p=56}} \right.$

To solve this, we want the coefficients of one of the variables to be the same. To make the coefficients of c the same, we can multiply the top equation by 2:

$\left \{ {{2(4c+6p=26)} \atop {8c+12p=56}} \right. \\\\\left \{ {{8c+12p=52} \atop {8c+12p=56}} \right.$

To cancel c, we will subtract the second equation from the first one. However, this also cancels p:

$\left \{ {{8c+12p=52} \atop {-(8c+12p=56)}} \right. \\\\0+0=-4\\0=-4$

We get a statement that is not true; thus the system has no solution, and we cannot solve for a unique amount of time.

Answer from: linsey9201

Step-by-step explanation:

Given :

Machine A ran for 26 hours and produced 4 cockpits and 6 propulsion systems.

Machine B ran for 56 hours and produced 8 cockpits and 12 propulsion systems.

To Find : Can we solve for a unique amount of time that it takes each machine to produce a cockpit and to produce a propulsion system?

Solution :

Let x be the time taken to produce 1 cockpits

So, time taken to produce 4 cockpits = 4x

So, time taken to produce 8 cockpits = 8x

Let y be the time taken to produce 1 Propulsion

So. time taken to produce 6 propulsion = 6y

So. time taken to produce 12 propulsion = 12y

Now we are given that Machine A ran for 26 hours and produced 4 cockpits and 6 propulsion systems.

⇒ 4x+6y =26 --a

We are also given that Machine B ran for 56 hours and produced 8 cockpits and 12 propulsion systems.

⇒ 8x+12y =56 --b

Solving equation a and b by substitution method

Substitute the value of x from equation in b

⇒ $8(\frac{26-6y}{4}) +12y =56$

⇒ 52-12y+12y =56

⇒ 52 =56

We get a statement that is not true; thus the system has no solution, and we cannot solve for a unique amount of time.

Answer from: Quest

1.0

step-by-step explanation:

Answer from: Quest

29. because you will divide each number of months by 12 to find the number of years. which would mean, 5, 12.5, 16, 45, 50, 72.5. which is crazy. anyhow, i think you find the median in the middle. and yea hope your test goes good

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