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?
enough already :(
Sorry lol
I posted this a few minutes before you answered, I really need it done
To solve this problem using substitution or elimination, let's first assign variables to the unknown quantities. Let's use:
x = number of racing bikes built
y = number of mountain bikes built
Using the given information, we can set up a system of equations.
Equation 1: Materials Cost: 110x + 140y = 26,150
Equation 2: Labor Cost: 120x + 180y = 31,800
Now, we can solve this system of equations either by substitution or elimination. Let's use the elimination method.
Multiplying Equation 1 by 3 and Equation 2 by 2, we can eliminate the y variable by adding the equations together.
3 * Equation 1: 3(110x + 140y) = 3 * 26,150
330x + 420y = 78,450
2 * Equation 2: 2(120x + 180y) = 2 * 31,800
240x + 360y = 63,600
Adding the modified equations together, we have:
(330x + 420y) + (240x + 360y) = 78,450 + 63,600
570x + 780y = 142,050
Now we have a new equation.
Next, let's solve the new equation for one variable (x or y). To make the calculation easier, let's divide the entire equation by 30.
(570x + 780y) / 30 = (142,050) / 30
19x + 26y = 4,735
Now we have another equation in terms of x and y.
From here, we can proceed with either substitution or elimination. Let's use substitution to solve for x.
Using Equation 2: 120x + 180y = 31,800
Rearranging it to solve for x, we have:
120x = 31,800 - 180y
x = (31,800 - 180y) / 120
x = (31,800 / 120) - (180y / 120)
x = 265 - (3/2)y
Now we have the value of x in terms of y.
Let's substitute this expression for x into the equation we obtained earlier (19x + 26y = 4,735) to solve for y.
19(265 - (3/2)y) + 26y = 4,735
Distributing, we have:
5,035 - 28.5y + 26y = 4,735
Combining like terms, we get:
-2.5y = -300
Dividing both sides by -2.5, we find:
y = 120
Now that we know the value of y, we can substitute it back into Equation 2 to find x:
120x + 180(120) = 31,800
120x + 21,600 = 31,800
120x = 10,200
x = 85
Therefore, the bicycle manufacturer built 85 racing bikes and 120 mountain bikes.