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?
Solve for using substitution or elimination
Hey, I just did this below
I need it to be solved using substitution or elimination
Oh, this is not good
120 nr + 180 nm = $31,800
110 nr + 140 nm = $26,150
is like
12 r + 18 m = 3180
11 r + 14 m = 2615
multiply top eqn by 11, bottom by 12
132 r + 198 m = 34980
132 r + 168 m = 31380
------------------------------------ subtract
30 m = 3600
3 m = 360
m = 120
NOW you can do it.
Thanks
You are welcome.
To find the number of racing bikes and mountain bikes built by the bicycle manufacturer, we can set up a system of equations based on the given information.
Let's assume the number of racing bikes built is 'x' and the number of mountain bikes built is 'y'.
Now we can start by setting up the equations for the total cost of labor and materials:
For labor:
120x + 180y = 31,800
For materials:
110x + 140y = 26,150
Now we can solve this system of equations to find the values of 'x' and 'y'.
We'll use the method of substitution:
From the first equation, we can solve for x in terms of y:
120x = 31,800 - 180y
x = (31,800 - 180y)/120
Substituting this value of x into the second equation:
110((31,800 - 180y)/120) + 140y = 26,150
Now we can simplify and solve for y:
Starting with the equation:
(31,800 - 180y)/120 = (26,150 - 140y)/110
Cross-multiplying, we get:
110(31,800 - 180y) = 120(26,150 - 140y)
Expanding and simplifying:
3,498,000 - 198,000y = 3,138,000 - 168,000y
Rearranging and simplifying:
30,000y = 360,000
y = 360,000 / 30,000
y = 12
Now we have found the number of mountain bikes built. Substituting this value of y back into the first equation, we can find the value of x:
120x + 180(12) = 31,800
120x + 2,160 = 31,800
120x = 31,800 - 2,160
120x = 29,640
x = 29,640 / 120
x = 246
So, the bicycle manufacturer built 246 racing bikes and 12 mountain bikes.