Question

McKenna and Lara work for their uncle Eddie who repairs skateboards and bicycles. Uncle Eddie is leaving for a vacation to the Amazon. He asks the girls to order 54 new wheels for 21 skateboards and bicycles in his repair shop. How many bicycles and how many skateboards are in uncle Eddies shop?

Answer 1

Let x be a number of skateboards and y be the number of bicycles in Eddie's repair shop.

Eddie asks the girls to order 54 new wheels for 21 skateboards and bicycles, then

x+y=21.

One scateboard has 4 wheels, then x scateboards have 4x wheels, one bicycle has 2 wheels, then y bicycles have 2y wheels. In total there should be ordered 54 wheels, so

4x+2y=54.

Solve the system of equations:

$\left\{\begin{array}{l}x+y=21\\4x+2y=54.\end{array}\right.$

From the first equation $x=21-y.$ Substitute it into the second equation:

$4(21-y)+2y=54,\\ \\84-4y+2y=54,\\ \\-2y=54-84,\\ \\-2y=-30,\\ \\2y=30,\\ \\y=15.$

Then

$x=21-15=6.$

Answer: 6 scateboards and 15 bicycles.