The price of a sweater is $5 less than twice the price of a jacket. If four sweaters and three jackets cost $200, what is the price of each jacket?

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Answer 1 · 2018-07-04T22:31:18

Let the prices be #S# and #J#

We know:
#S=2J-5#
#4S+3J=200#

We substitute #S# in the second equation with #2J-5# from the first equation:
#4(2J-5)+3J=200->#

Brackets:
#8J-20+3J=200->#
#11J-20=200->#

Add #20# on both sides:
#11J-cancel20+cancel20=200+20=220#

Divide by #11#:
#(cancel11J)/cancel11=220/11->J=20->#

#S=2J-5=2*20-5->S=35#

Conclusion:
A jacket costs #$20# and a sweater costs #$35#

Check your answer!
#4xx$35+3xx$20=$140+$60=$200#