19 Jun There were ##18## skiers and ##10## snowborders. Assume ther
There were ##18## skiers and ##10## snowborders. Assume there were ##X## skis and ##Y## snowboards rented. Since there were ##28## people who rented equipment we have the first equation: ##X+Y=28## Considering the price of ##$16## per ski and ##$19## per snowboard and the total amount resort has got is ##$478## we have the second equation: ##16X+19Y=478## To solve this system of two linear equations with two unknowns we will use the method of substitution – resolve the first equation for ##Y## in therms of ##X## and substitute it into the second equation thus getting one equation with one unknown. From the first equation adding ##-X## to both sides we get: ##-X+X+Y=-X+28## or cancelling ##-X+X## because it’s equal to 0 ##Y=-X+28=28-X## Substitute this expression for ##Y## into the second equation: ##16X+19(28-X)=478## Using distributive law ##a(b+c)=ab+ac## the latter is: ##16X+19*28-19X=478## Using commutative law of addition we can change the sequence of operation. Also perform the multiplication: ##16X-19X+532=478## Using the distributive law we can combine ##16X-19X##: ##(16-19)X+532=478## Subtract ##478## from both sides of this equation and perform ##16-19## operation: ##-3X+532-478=478-478## or ##-3X+54=0## Adding ##3X## to both sides yields: ##3X-3X+54=3X## or ##54=3X## Dividing by ##3## both sides of this equation ##18=X## From this we can find ##Y=-X+28##: ##Y=-18+28=10## CHECKING: ##18## (skis) ##+## ##10## (snowboards) = ##28## (CHECK!) ##18*$16= $288## (skis total) ##10*$19=$190## (snowboards total) ##$288+$190=$478## (total rent) (CHECK!)
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