Setting Up Correct Equation...1

[mathdad]

For questions 58, 60, and 62, set up the correct equations. Use any variable(s) of choice.

58. The length of fence required to enclose a rectangular field is 3000 meters. What are the dimensions of the field if it is known that the difference between its length and width is 50 meters?

Set Up:

P = 2L + 2W

Length = (x - 50)

Width = x

3000 = 2(x - 50) + 2x

60. A movie theater charges 9.00 for adults and 7.00 for senior citizens. On a day when 325 people paid for admission, the total receipts were 2495. How many who paid were adults? How many were seniors?

Set Up:

Let a = adults

Let s = senior citizens

a + s = 325
9a + 7s = 2495

62. A chemist wants to make 14 liters of a 40 percent acid solution. She has solutions that are 30 percent acid and 65 percent acid. How much of each must she mix?

Set Up:

Let x = amount of acid to mix

14(0.40) = 0.30x + 0.65x

Is any of this correct?

 

[JeffM]

# 58 looks good.

 

[Dr.Peterson]

58. The length of fence required to enclose a rectangular field is 3000 meters. What are the dimensions of the field if it is known that the difference between its length and width is 50 meters?

Set Up:
P = 2L + 2W
Length = (x - 50)
Width = x
3000 = 2(x - 50) + 2x

I personally would have defined x first, since as it is you've used a variable that is not defined (yet):

Width (in meters) = x​

Length (in meters)= x - 50 [i.e. length is 50 m less than width]​

Also, though it doesn't ultimately matter, it's worth being aware that you have chosen to say that the length is shorter than the width. Some people would want the length to be longer; that's not necessary, but it might surprise you are the end if you weren't aware of it. Also, observe that I find it very helpful to include the units in the definition, which is very useful when I need to state the answer (was this in meters or pounds ... ?).

60. A movie theater charges 9.00 for adults and 7.00 for senior citizens. On a day when 325 people paid for admission, the total receipts were 2495. How many who paid were adults? How many were seniors?

Set Up:
Let a = adults
Let s = senior citizens
a + s = 325
9a + 7s = 2495

Although I might well write it like this for my own use, it's good for the sake of communication to clarify:

Let a = number of adults​

Let s = number of senior citizens​

Otherwise, good. (But as a senior citizen, am I not an adult? ...)

62. A chemist wants to make 14 liters of a 40 percent acid solution. She has solutions that are 30 percent acid and 65 percent acid. How much of each must she mix?

Set Up:
Let x = amount of acid to mix
14(0.40) = 0.30x + 0.65x

This one is not good. There are two different solutions, and nothing says she uses the same amount of each, so each needs its own variable. The question "How much of each ..." is a clue that something is wrong, if you didn't catch it earlier.

 

[mathdad]

I personally would have defined x first, since as it is you've used a variable that is not defined (yet):

Width (in meters) = x​

Length (in meters)= x - 50 [i.e. length is 50 m less than width]​

Also, though it doesn't ultimately matter, it's worth being aware that you have chosen to say that the length is shorter than the width. Some people would want the length to be longer; that's not necessary, but it might surprise you are the end if you weren't aware of it. Also, observe that I find it very helpful to include the units in the definition, which is very useful when I need to state the answer (was this in meters or pounds ... ?).


Although I might well write it like this for my own use, it's good for the sake of communication to clarify:

Let a = number of adults​

Let s = number of senior citizens​

Otherwise, good. (But as a senior citizen, am I not an adult? ...)


This one is not good. There are two different solutions, and nothing says she uses the same amount of each, so each needs its own variable. The question "How much of each ..." is a clue that something is wrong, if you didn't catch it earlier.

For 62, the second equation should be x + y = 14.