it costs $0.55 for domestic mail within Australia and $2.05 to post to Europe

i have been given this question for my uni course and i have no idea how to do it:

it costs $0.55 for domestic mail within Australia and $2.05 to post a letter to Europe. If i spent $10 to post 10 letters how many of each type did i post?

i need to figure this out using algebra.

i know the answer which you would like could make it easy but no i cant get the computation

Bella310179 said:

i have been given this question for my uni course and i have no idea how to do it:

it costs $0.55 for domestic mail within Australia and $2.05 to post a letter to Europe. If i spent $10 to post 10 letters how many of each type did i post?

i need to figure this out using algebra.

i know the answer which you would like could make it easy but no i cant get the computation

Click to expand...

Start with naming your variables (things that you need to calculate)

No of letters in domestic mail = D

No of letters in international mail = I

Then

I + D = 10 ..... continue

What are your thoughts?

Please share your work with us ...even if you know it is wrong

If you are stuck at the beginning tell us and we'll start with the definitions.

You need to read the rules of this forum. Please read the post titled "Read before Posting" at the following URL:

http://www.freemathhelp.com/forum/th...Before-Posting

Bella310179 said:

i have been given this question for my uni course and i have no idea how to do it:

Click to expand...

Then the first step is to study so you can get an "idea how to do it". This sort of exercise is probably expecting you to set up equations for a "mixture" kind of exercise, because you're mixing two different items in a total purchase. There are lessons available online for this topic; try here.

Bella310179 said:

it costs $0.55 for domestic mail within Australia and $2.05 to post a letter to Europe. If i spent $10 to post 10 letters how many of each type did i post?

Click to expand...

Once you have studied at least two lessons from the link, please attempt the exercise. You can get it started like this:

number of Australian letters: a
number of European letters: e = 10 - a

...and go from there. If you get stuck, please reply showing your work so far, starting from the above selection of variables. Thank you!

So far i have
10 = 2.05x - 0.55y
X + y = 10
X = 10- y
10 = 2.05 (10 - y) - 0.55y
= 20.5 - 2.6y

This is wherei come undone. I know this wont give me the correct answer. I know it is 3 to europe 7 to domestic...

Thanks

i already have the
a + b = 10
b = 10 - a

or is i let europe be x
number of domestic = 10 - x
total cost is 2.05x = 0.55 (10 - x) = $10.00
2.05x - 2x = 10 -5.50
2x= 4.50
x= 2.25

BUT this is not the answer i know the answer is 3 europe and 7 domestic... this is why i am so stuck

is it as simple as swapping and doing 0.55x - 2.05(10-x) = 10

i just dont know.

Bella310179 said:

So far i have
10 = 2.05x - 0.55y

Click to expand...

On what basis have you subtracted the cost of in-country mailing from the cost of mailing to Europe? Where does the exercise state that the difference in costs was ten dollars?

Bella310179 said:

X + y = 10
X = 10- y
10 = 2.05 (10 - y) - 0.55y
= 20.5 - 2.6y

This is wherei come undone.

Click to expand...

You "came undone"? How so? What happened next, when you went to solve the linear equation?

Bella310179 said:

i already have the
a + b = 10
b = 10 - a

or is i let europe be x
number of domestic = 10 - x
total cost is 2.05x = 0.55 (10 - x) = $10.00

Click to expand...

How did you get that the cost of mailing to Europe equals the cost of mailing within Australia, and that each of these equals the total for both? How does this make sense?

Bella310179 said:

i know the answer is 3 europe and 7 domestic...

Click to expand...

Check this proposed solution:

. . . . .2.05(3) + 0.55(7) = 6.15 + 3.85 = 10

So this answer does indeed "check".

To do this yourself, try studying a lesson or two at the link, re-reading the hints and helps, and then writing out, very explicitly, what exactly you mean by each variable, expression, and equation. When you know what you mean going in, you're more likely to arrive at something sensible when you come out the other end.

I think I will just have to leave this. I am finding this more confusing than the actual question. I understand there are errors in my calculations but this is why i was asking for help as i really dont understand how or why.
Thanks anyway

Denis. Thank you so much.
Ill rework soon and post.

Ok Denis. I followed everything but no luck.

D=0.55 e=2.05

Post 10 for $10

D + e = 10
E = 10-d

0.55d + 2.05e = $10
0.55d + 2.05(10-d) =$10
0.55d + 20.50 - 2.05d = $10
0.55d-2.05d= 10-20.50
-d= -10.50
D= 10.50

Now clearly this isn't correct.

Even if i do the numbers the other way still now joy i get 4.5 which isnt right either. Even if i round up its still not the right answer. I cant figure out where i am going so wrong.

Bella310179 said:

Ok Denis. I followed everything but no luck.

D=0.55 e=2.05 ..... This is not correct!

'D' (NUMBER of domestic stamps) and 'e' (NUMBER of european stamps) are UNKNOWNS that you need to calculate.

You are mixing up the PRICE of the stamps with the NUMBER of stamps.

Post 10 for $10

D + e = 10
E = 10-d

0.55d + 2.05e = $10
0.55d + 2.05(10-d) =$10
0.55d + 20.50 - 2.05d = $10
0.55d-2.05d= 10-20.50
-d= -10.50
D= 10.50

Now clearly this isn't correct.

Even if i do the numbers the other way still now joy i get 4.5 which isnt right either. Even if i round up its still not the right answer. I cant figure out where i am going so wrong.

Click to expand...

I'll do the problem for you.

D = number of domestic stamps

e = number of european stamps

D + e = 10 ..............................................................(1)

D = 10 - e ...............................................................(2)

Then considering the cost

0.55*D + 2.05*e = 10 ................................................(3)

Using (2) in (3)

0.55 * (10 - e) + 2.05*e = 10

-0.55 * e + 5.5 + 2.05*e = 10

1.5 * e = 4.5

e = 3 .....................................................................(4)

Now use (4) into (2) to calculate 'D'

Then use the calculate values of 'e' and 'D' in (1) and (3) to check your solution.

Bella310179 said:

Ok Denis. I followed everything but no luck.

D=0.55 e=2.05

Click to expand...

From the above, it appears that you have used variables to stand for the known costs of mailing. Why?

Bella310179 said:

Post 10 for $10

D + e = 10

Click to expand...

From the above, it appears that you have re-defined the variables to stand for the number of items mailed. Which variable stands for which?

Bella310179 said:

E = 10-d

Click to expand...

From the above, it appears that you have re-named the variables, or perhaps have switched to different variables (since "D" is the not the same as "d", and "E" is not the same as "e"). Why? What are the definitions of the new variables?

Bella310179 said:

0.55d + 2.05e = $10

Click to expand...

From the above, it appears that you have settled on "d" and "e" for your variables, and I think you mean "d" to stand for the number of "domestic" mailings and "e" to stand for the number of "European" mailings. The equation appears to stand for the mailing costs.

Bella310179 said:

0.55d + 2.05(10-d) =$10
0.55d + 20.50 - 2.05d = $10
0.55d-2.05d= 10-20.50
-d= -10.50

Click to expand...

How did you get that 0.55 - 2.05 somehow equaled -1?

Bella310179 said:

D= 10.50

Click to expand...

Why have you switched back to the old variable "D"? For what does it stand?

When it was suggested that you try "writing out, very explicitly, what exactly you mean by each variable, expression, and equation," the step-by-step reasoning provided by some of the helpers was what was meant. Try modelling on that.