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:
[tex]\left\{\begin{array}{l}x+y=21\\4x+2y=54.\end{array}\right.[/tex]
From the first equation [tex]x=21-y.[/tex] Substitute it into the second equation:
[tex]4(21-y)+2y=54,\\ \\84-4y+2y=54,\\ \\-2y=54-84,\\ \\-2y=-30,\\ \\2y=30,\\ \\y=15.[/tex]
Then
[tex]x=21-15=6.[/tex]
Answer: 6 scateboards and 15 bicycles.
