SOLUTION: Hats cost 15 dollars each, and ties cost 20 dollars each. John spent 250 dollars buying hats and ties. He bought a total of 15 items. How many hats and how many ties did he buy?

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Question 783791: Hats cost 15 dollars each, and ties cost 20 dollars each. John spent 250 dollars buying hats and ties. He bought a total of 15 items. How many hats and how many ties did he buy?
Answer by josgarithmetic(39625) About Me  (Show Source):
You can put this solution on YOUR website!
Most important goal is form two simultaneous equations in two variables.

x = count of hats
y = count of ties

Account for the cost: 15x%2B20y=250
This should immediately be simplified so it is easier to use in solving the system. Divide left and right by 5>....
3x%2B4y=50

Account for total quantity of items bought: x%2By=15

Solve this system in any way you want:
highlight%283x%2B4y=50%29
highlight%28x%2By=15%29




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recommendation: multiply the "15" equation by 3, and then subtract from the "50" equation; and immediately find value for y....