Finite Question

Question

City and Country Cycles sells two kinds of bicycles, mountain bikes and racing bikes. They have $63,000 to spend on new bikes and 390 hours of assembly time to put them together. Each mountain bike costs $300 wholesale and takes two hours to assemble. Each racing bike costs $420 wholesale and takes two-and-one-half hours to assemble. How many of each can the shop buy and assemble to use all available money and time?

Answer 1

Let x = number of mountain bikes and let y = number of racing bikes.

 

The amount of time it will take to put all the bikes together must equal 390 hours. So:

 

2x + 2.5y = 390

 

The amount of money it will take to buy all the bikes must equal $63,000. So:

 

300x + 420y = 63000

 

 

 

Now you have a system of equations:

 

2x + 2.5y = 390

300x + 420y = 63000

 

Solve the first equation for x, then plug that into the second equation and solve for y:

 

2x = 390 - 2.5y

x = 195 - 1.25y

 

300x + 420y = 63000

300(195 - 1.25y) + 420y = 63000

58500 - 375y + 420y = 63000

58500 + 45y = 63000

45y = 4500

y = 100

 

Now, plug that value into the first equation to solve for x:

 

2x + 2.5(100) = 390

2x + 250 = 390

2x = 140

x = 70

 

 

 

The shop can buy and assemble x = 70 mountain bikes and y = 100 racing bikes.