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?
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Let x = no. of shirts sold
let y = no. of ties
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"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({{{x/3}}}) + 2y = 1000
{{{(10x)/3}}} + 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?"
{{{1/2}}}*{{{(10x)/3}}} + {{{2/3}}}*2y = 600
{{{(10x)/6}}} + {{{(4y)/3}}} = 600
Reduce fraction
{{{(5x)/3}}} + {{{(4y)/3}}} = 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
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Find x, use eq: 10x + 6y = 3000
10x + 6(300) = 3000
10x + 1800 = 3000
10x = 3000 - 1800
10x = 3000 - 1800
10x = 1200
x = {{{1200/10}}}
x = 120 shirts sold
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Check solution in 
5x + 4y = 1800
5(120) + 4(300) = 
600 + 1200 = 1800