SOLUTION: A shipment of 21 computer keyboards and 33 monitors cost $35564.25. Another shipment of 41 keyboards and 36 monitors cost $49503.08. Find the cost of each keyboard and each monitor

Algebra ->  Proportions -> SOLUTION: A shipment of 21 computer keyboards and 33 monitors cost $35564.25. Another shipment of 41 keyboards and 36 monitors cost $49503.08. Find the cost of each keyboard and each monitor      Log On


   



Question 909126: A shipment of 21 computer keyboards and 33 monitors cost $35564.25. Another shipment of 41 keyboards and 36 monitors cost $49503.08. Find the cost of each keyboard and each monitor.
Found 3 solutions by richwmiller, josmiceli, clearblueskai:
Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
21k+33m=$35564.25
41k+36m=$49503.08
k=591.77 Those are expensive keyboards
m=701.12
21*591.77=12427.17
33*701.13=23137.29
35564.46
41*591.77=24262.57
36*701.12=25240.32
49502.89

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +k+ = cost of a keyboard
Let +m+ = the cost of a monitor
------------------------------
(1) +21k+%2B+33m+=+35564.25+
(2) +41k+%2B+36m+=+49503.08+
--------------------------
Divide both sides of (1) by +11+
Divide both sides of (2) by +12+
------------------------------
(1) +%2821k%29%2F11+%2B+3m+=+35564.25%2F11+
(2) +%2841k%29%2F12+%2B+3m+=+49503.08%2F12+
------------------------------------
Subtract (1) from (2)
(2) +%2841k%29%2F12+%2B+3m+=+49503.08%2F12+
(1) +-%2821k%29%2F11+-+3m+=+-35564.25%2F11+
------------------------------------
+%28+41k+%29%2F12++-+%28+21k+%29%2F11+=+49503.08%2F12+-+35564.25%2F11+
Multiply both sides by +12%2A11+
+11%2A41k+-+12%2A21k+=+11%2A49503.08+-+12%2A35564.25+
+451k+-+252k+=+544533.88+-+426771+
+199k+=+117762.88+
+k+=+591.77326+
---------------------
Plug this back into either equation to find +m+
check my math, too

Answer by clearblueskai(22) About Me  (Show Source):
You can put this solution on YOUR website!
A shipment of 21 computer keyboards and 33 monitors cost $35564.25. Another shipment of 41 keyboards and 36 monitors cost $49503.08. Find the cost of each keyboard and each monitor.
x - cost of each keyboard
y - cost of each monitor
21x%2B33y=35564.25
41x%2B36y=49503.08
Subtitution:
y=+%28%2835564.25%29-21x%29%2F33
41x%2B36%28%28%2835564.25%29-21x%29%2F33%29=49503.08
x=591.773
y=%28%2835564.25%29-21%28591.773%29%29%2F33
y=701.122