SOLUTION: I subscribe to the Comic-of-the-Month Club. Each month I can buy any number of the 48 titles offered by the club. The first month I bought five comics for $19.07. The s

Algebra ->  Customizable Word Problem Solvers  -> Finance -> SOLUTION: I subscribe to the Comic-of-the-Month Club. Each month I can buy any number of the 48 titles offered by the club. The first month I bought five comics for $19.07. The s      Log On

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Question 1098463: I subscribe to the Comic-of-the-Month Club. Each month I can buy any number of the 48 titles offered by the club. The first month I bought five comics for $19.07. The second month I bought two comics for $8.72. The next month I bought six of the club offerings for $22.52. In May I bought three more for $12.17. The club charges a fee for each comic and a handling fee for the entire order. How much would it have cost to buy all 48 titles at the same time
Found 2 solutions by josmiceli, richwmiller:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = the price of 1 comic
Let +b+ = the fee for 1 comic
Let +c+ = the handling fee/order
-----------------------------------
1st month:
(1) +5%2A%28+a+%2B+b+%29+%2B+c+=+19.07+
2nd month:
(2) +2%2A%28+a+%2B+b+%29+%2B+c+=+8.72+
3rd month:
(3) +6%2A%28+a+%2B+b+%29+%2B+c+=+22.52+
May order:
(4) +3%2A%28+a+%2B+b+%29+%2B+c+=+12.17+
-----------------------------
Multiply both sides of (2) by +3+
and subtract (3) from (2)
(2) +6%2A%28+a+%2B+b+%29+%2B+3c+=+26.16+
(3) +-6%2A%28+a+%2B+b+%29+-+c+-+22%2C52+
---------------------------------
+2c+=+3.64+
+c+=+1.82+
-----------------
(1) +5%2A%28+a+%2B+b+%29+%2B+1.82+=+19.07+
(1) +5%2A%28+a+%2B+b+%29+=+17.25+
and
(2) +2%2A%28+a+%2B+b+%29+%2B+1.82+=+8.72+
(2) +2%2A%28+a+%2B+b+%29+=+6.9+
------------------------------
Multiply both sides of (2) by +2+
and subtract (2) from (1)
(1) +5%2A%28+a+%2B+b+%29+=+17.25+
(2) +4%2A%28+a+%2B+b+%29+=+13.8+
------------------------------
+a+%2B+b+=+3.45+
---------------------------
For all 48 titles ordered at the same time:
+C+=+48%2A%28+a+%2B+b+%29+%2B+c+
+C+=+48%2A3.45+%2B+1.82+
+C+=+165.6+%2B+1.82+
+C+=+167.42+
$167.42 for the order
------------------------
check:
(4) +3%2A%28+a+%2B+b+%29+%2B+c+=+12.17+
(4) +3%2A3.45+%2B+1.82+=+12.17+
(4) +10.35+%2B+1.82+=+12.17+
(4) +12.17+=+12.17+
OK
You can check (1), (2), (3)
---------------------------
Note that there is no way to separate
+a+ and +b+ to find what they are,
but you don't have to to solve the problem.
Feel free to get another opinion and
check my math

Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
5c+h=19.07
2c+h=8.72
6c+h=22.52
3c+h=12.17
6c+2h=24.34
6c+h=22.52
h=24.34-22.52
h=1.82
check
5c+1.82=19.07
5c=19.07-1.82=17.25
c=17.25/5
c=3.45
2c+h=8.72
2*3.45+1.82=8.72
6c+h=22.52
6*3.45+1.82=22.52
3c+h=12.17
3*3.45+1.82=12.17
ok
48c+1.82
48*3.45+1.82=$167.42 to buy all 48 at once