SOLUTION: A merchant sold his entire stock of shirts and ties for $1000, the shirts being priced at 3 for $10 and the ties at $2 each. If he had sold only 1/2 of the shirts and 2/3 of the ti
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Question 151377: A merchant sold his entire stock of shirts and ties for $1000, the shirts being priced at 3 for $10 and the ties at $2 each. If he had sold only 1/2 of the shirts and 2/3 of the ties he would have collected $600. How many of each kind did he sell?
Found 2 solutions by ankor@dixie-net.com, stanbon:
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
A merchant sold his entire stock of shirts and ties for $1000, the shirts being priced at 3 for $10 and the ties at $2 each. If he had sold only 1/2 of the shirts and 2/3 of the ties he would have collected $600. How many of each kind did he sell?
;
Let x = no. of shirts sold
let y = no. of ties
:
"A merchant sold his entire stock of shirts and ties for $1000, the shirts being priced at 3 for $10 and the ties at $2 each"
10() + 2y = 1000
+ 2y = 1000
multiply equation by 3 to get rid of the denominator
10x + 6y = 3000; (1st equation)
:
"If he had sold only 1/2 of the shirts and 2/3 of the ties he would have collected $600. How many of each kind did he sell?"
* + *2y = 600
+ = 600
Reduce fraction
+ = 600
Multiply equation by 3 to get rid of the denominator
5x + 4y = 1800
:
multiply above equation by 2 and subtract the 1st equation:
10x + 8y = 3600
10x + 6y = 3000
-----------------subtraction eliminates x
0x + 2y = 600
y = 300 ties sold
:
Find x, use eq: 10x + 6y = 3000
10x + 6(300) = 3000
10x + 1800 = 3000
10x = 3000 - 1800
10x = 3000 - 1800
10x = 1200
x =
x = 120 shirts sold
:
:
Check solution in
5x + 4y = 1800
5(120) + 4(300) =
600 + 1200 = 1800
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
A merchant sold his entire stock of shirts and ties for $1000, the shirts being priced at 3 for $10 and the ties at $2 each.
Value Equation 1: (10/3)s + 2t = 1000
--------------------------
If he had sold only 1/2 of the shirts and 2/3 of the ties he would have collected $600.
Value Equation 2: (10/3)(s/2) + 2(2/3)t = 600
--------------------------
How many of each kind did he sell?
----------
Rearrange the equations:
Eq 1: 10s + 6t = 3000
Eq 2: 5s + 4t = 1800
------------
Set-up for elimination:
10s + 6t = 3000
10s + 8t = 3600
-----------------
Subtract to get:
2t = 600
t = 300 (# of ties sold)
---------------------
Since 5s + 4t = 1800 ,
5s + 4*300 = 1800
5s = 600
s = 120 (# of shirts sold)
=============================
Cheers,
Stan H.
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