SOLVE FOR USING SUBSTITUTION OR ELIMINATION
A bicycle manufacturer builds racing bikes and mountain bikes. Materials for the racing bike cost $110 while labor to build them is $120. Materials for the mountain bike cost $140 and labor is $180. The company budgeted $31,800 for labor and $26,150 for materials. How many of each bicycle did they build?
see below for 120 mountain bikes, then finish it.
To solve this problem using substitution or elimination method, you can create a system of equations to represent the given information.
Let's denote the number of racing bikes as 'r' and the number of mountain bikes as 'm'.
The problem states that materials for the racing bike cost $110 and the labor costs $120. Hence, the total cost for 'r' racing bikes would be 110r for materials and 120r for labor.
Similarly, the total cost for 'm' mountain bikes would be 140m for materials and 180m for labor.
The company budgeted $31,800 for labor, so we can write the first equation:
120r + 180m = 31,800
The company budgeted $26,150 for materials, so we can write the second equation:
110r + 140m = 26,150
Now, we have a system of equations:
120r + 180m = 31,800
110r + 140m = 26,150
We can now solve this system using substitution or elimination method. I will demonstrate the elimination method.
Multiply the first equation by 11 and the second equation by 12 to eliminate the variable 'r':
(11)(120r + 180m) = (11)(31,800)
(12)(110r + 140m) = (12)(26,150)
This simplifies to:
1320r + 1980m = 349,800
1320r + 1680m = 313,800
Now, subtract the second equation from the first equation to eliminate 'r':
(1320r + 1980m) - (1320r + 1680m) = 349,800 - 313,800
This simplifies to:
300m = 36,000
Divide both sides of the equation by 300:
m = 120
Now that we have the value of 'm', we can substitute it back into either equation to find the value of 'r'. Let's substitute it into the first equation:
120r + 180(120) = 31,800
This simplifies to:
120r + 21,600 = 31,800
Subtract 21,600 from both sides:
120r = 10,200
Divide both sides by 120:
r = 85
Therefore, the company built 85 racing bikes and 120 mountain bikes.