Set Up Correct Equations...3

mathdad

mathdad

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Do not solve. Set up the correct equations.

To manufacture an automobile requires
painting, drying, and polishing. Epsilon Motor Company produces three types of cars, the Delta, the Beta, and the Sigma. Each Delta requires 9 hours for painting, 2 hours for drying, and 3 hours for polishing. A Beta requires 33 hours for painting, 8 hours for drying, and 4 hours for polishing, and a Sigma requires 8 hours for painting, 1 hour for drying, and 2 hours for polishing. If the company has 419 hours for painting, 89 hours for drying, and 68 hours for polishing per month, how many of each type of car are produced?

My Work:

Let x = painting

Let y = drying

Let z = polishing

9x + 33y + 8z = 419
2x + 8y + z = 89
3x + 4y + 2z = 68

Correct?
 
mathdad said:
Do not solve. Set up the correct equations.

To manufacture an automobile requires
painting, drying, and polishing. Epsilon Motor Company produces three types of cars, the Delta, the Beta, and the Sigma. Each Delta requires 9 hours for painting, 2 hours for drying, and 3 hours for polishing. A Beta requires 33 hours for painting, 8 hours for drying, and 4 hours for polishing, and a Sigma requires 8 hours for painting, 1 hour for drying, and 2 hours for polishing. If the company has 419 hours for painting, 89 hours for drying, and 68 hours for polishing per month, how many of each type of car are produced?

My Work:
Let x = painting
Let y = drying
Let z = polishing
9x + 33y + 8z = 419
2x + 8y + z = 89
3x + 4y + 2z = 68
Click to expand...
Correct? No!

You said "x = painting" - painting what?

- money spent on painting?
​
- money earned from painting?
​
- #of painting eaten by the goat tethered to the fence?​
 
mathdad said:
Do not solve. Set up the correct equations.

To manufacture an automobile requires
painting, drying, and polishing. Epsilon Motor Company produces three types of cars, the Delta, the Beta, and the Sigma. Each Delta requires 9 hours for painting, 2 hours for drying, and 3 hours for polishing. A Beta requires 33 hours for painting, 8 hours for drying, and 4 hours for polishing, and a Sigma requires 8 hours for painting, 1 hour for drying, and 2 hours for polishing. If the company has 419 hours for painting, 89 hours for drying, and 68 hours for polishing per month, how many of each type of car are produced?

My Work:

Let x = painting

Let y = drying

Let z = polishing

9x + 33y + 8z = 419
2x + 8y + z = 89
3x + 4y + 2z = 68

Correct?
Click to expand...
"Painting" is not a quantity, so x can't be defined as "painting". Do you mean "x = time spent painting"? They've already told you that.

What are they asking for? "How many of each type of car are produced?" So your variables should be the number of each type of car!

If you defined the variables that way, then your equations would actually be correct. But since you didn't, they are nonsense, and I get the impression you just stuck some numbers together in a way that looks right, but without actually thinking.

What does the first equation mean? By your variable definitions, 9x would mean 9 hours of painting per Delta produced, times "painting", whatever that means. By the right definitions, 9x would mean 9 hours of painting per Delta produced, times the number of Deltas produced, which is the number of hours spent painting Deltas. Adding that to 33y and 8z would give the total number of hours spent painting, which is indeed 419.

Do you see the utter necessity of defining variables correctly?
 
Dr.Peterson said:
"Painting" is not a quantity, so x can't be defined as "painting". Do you mean "x = time spent painting"? They've already told you that.

What are they asking for? "How many of each type of car are produced?" So your variables should be the number of each type of car!

If you defined the variables that way, then your equations would actually be correct. But since you didn't, they are nonsense, and I get the impression you just stuck some numbers together in a way that looks right, but without actually thinking.

What does the first equation mean? By your variable definitions, 9x would mean 9 hours of painting per Delta produced, times "painting", whatever that means. By the right definitions, 9x would mean 9 hours of painting per Delta produced, times the number of Deltas produced, which is the number of hours spent painting Deltas. Adding that to 33y and 8z would give the total number of hours spent painting, which is indeed 419.

Do you see the utter necessity of defining variables correctly?
Click to expand...

In that case, x = Delta cars, y = Beta cars and z = Sigma cars.

9x + 33y + 8z = 419
2x + 8y + z = 89
3x + 4y + 2z = 68
 
mathdad said:
In that case, x = Delta cars, y = Beta cars and z = Sigma cars.

9x + 33y + 8z = 419
2x + 8y + z = 89
3x + 4y + 2z = 68
Click to expand...
I think you mean,

In that case, x = # of Delta cars, y = # of Beta cars and z = # of Sigma cars.
 
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