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 $S$ $S$ and $J$ $J$

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

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

Brackets:
$8 J - 20 + 3 J = 200 \to$ $8J-20+3J=200->$
$11 J - 20 = 200 \to$ $11J-20=200->$

Add $20$ $20$ 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=$200$