Split - Word Problem [2]

[Joanie10]

Sorry if I am not posting right; this is new to me. I need to know how to work this problem. The zoo charges $28 for each adult and $12 for each child. the total bill for 254 people was $3864. How many adults and how many children went to the zoo?

 

[mmm4444bot]

On the index pages, you will find the [newtopic] button. If you use it, then your post will appear as its own thread versus being appended to the end of somebody else's discussion.

With almost all word problems in algebra, we need to begin by assigning a symbol for each unknown value that we're asked to find.

This exercise asks for the number of adults and the number of children for whom tickets were bought.

Let a = the number of adults

Let c = the number of children

Now that we have symbols to work with, we can write two equations related to the given information.

a + c = 254

28a + 12c = 3864

Do you know how to solve this system of two equations for the values of a and c ? (You did not specify what help you need, so I'm not sure if you're good to go with my setup.)

I welcome your specific questions, if you need more help or further explanation. Please show your work.

 

[Joanie10]

Thank you so much for your help. I am an online student of age 70 and it has been a long time since I had algebra. Yes, I can work problems in the system you mentioned. I apparently was trying to use the wrong combination of variables. You most likely saved my grade. This problem is part of an essay I have to write this week and I was becoming very stressed out over it. Again thank you. Thank you also for telling me how to post correctly which I shall do nex time.

 

[Edith]

Congratulations for this great effort! Age is not a constrain while it comes to education and you have proved it. Nowadays, children are very likely to avoid math. I don't know why. Anyway, if you need further assistance with your math problems, you can surf the net. There are several online tutoring services available (SPAM removed) to help adult students learning math and encourage adult education.

 

[Sandrine2u]

Okay, I didn't get how 28a and 12c were selected. Why did you choose those numbers and what do you afterwards to get a quick answer? I'm studying for the GRE so is there a way to figure this problem out quickly and accurately?
I've tried some pretty high numbers, such as 28*44 +12*44 and I still don't get answer even close to 3864. Please help. Thank you.
28(a) + 12(c)=3864
28 (44) + 12(44) = 1760 - not the answer

 

[Deleted member 4993]

Okay, I didn't get how 28a and 12c were selected. Why did you choose those numbers and what do you afterwards to get a quick answer? I'm studying for the GRE so is there a way to figure this problem out quickly and accurately?
I've tried some pretty high numbers, such as 28*44 +12*44 and I still don't get answer even close to 3864. Please help. Thank you.
28(a) + 12(c)=3864
28 (44) + 12(44) = 1760 - not the answer

Why are you putting same number (44) for 'a' and 'c' - nothing in the problem says those are equal.

You are given two linear equations with two unknowns. Those equations can be solved by:

- Method of substitution

- Method of elimination

- Matrix manipulation

Does any of those methods sound familiar? You have encountered those in high-school algebra.

If those don't sound familiar - brush up through text-books.

In addition, you may want to go to:

http://www.purplemath.com/modules/systlin1.htm

for some refresher

 

[mmm4444bot]

I [don't] get how 28a and 12c were selected.

Two different dollar amounts comprise the total bill of $3864, for this group of 254 zoo visitors.

One amount is the cost for all of the adults; the other amount is the cost for all of the children.

The product 28a represents the total cost for all of the adult tickets.

Remember? We designated the symbol a to represent the number of adult tickets.

a tickets times 28 dollars (each) gives the cost for all of the adult tickets: 28a dollars.

Likewise, the product 12c represents the rest of the bill (i.e., 12c dollars is the cost for all of the children's tickets).

Therefore, 28a dollars plus 12c dollars must equal the total cost of the bill. I hope that the second equation makes sense to you, now. If you are still uncertain, please ask specific questions.

a + c = 254

28a + 12c = 3864

I don't know what's "quick" (use a calculator that has been programmed to do it for you, perhaps?), but I do know "accurate".

"Accurate" is what you get when you properly execute algorithmic steps from a method that you understand.



My point is that learning methods comes first; comparisons between methods come second.

I will use the Substitution Method to solve an example system for you. (You should also check out the link provided by Subhotosh; one does not develop understanding about this stuff from a single exposure.)

x + y = 36

44x - 70y = 1128

Step 1: Solve the first equation for y, in order to find an equivalent expression for y that contains no symbols "y".

y = 36 - x

Step 2: Replace the symbol y in the second equation with its equivalent expression (36 - x), in order to obtain an equation that contains only the variable x.

44x - 70(36 - x) = 1128

Step 3: Solve this new equation for x, in the usual way.

x = 32

Step 4: Substitute this x-value into the equivalent expression for y, to evaluate y.

y = 36 - x

y = 36 - 32

y = 4

Step 5: Check the solution x = 32 and y = 4 by substitution into the original system, to make sure that these values produce true statements.

x + y = 36
32 + 4 = 36
36 = 36

44x - 70y = 1128
44(32) - 70(4) = 1128
1408 - 280 = 1128
1128 = 1128

I welcome specific questions.

 

[Sandrine2u]

Never mind, I got it. a = # of adults and c= of children. c=203 and a=51. Thanks for helping with the set up.

 

[mmm4444bot]

Never mind, I got it.

By brute force?