a) Let's use the variables "ca" and "ta" to represent the number of cars and trucks sold by Dealership A, respectively. The equation for the total cars and trucks for Dealership A can be written as:
ca + ta = 164
b) Using the same logic, let's use the variables "cb" and "tb" to represent the number of cars and trucks sold by Dealership B, respectively. The equation for the total cars and trucks for Dealership B can be written as:
cb + tb = 229
c) From the given information, we know that Dealership A sells a total of 164 cars and trucks. We can use the equation we defined in part a) to solve for the number of cars (ca) sold by Dealership A:
ca + ta = 164
ca + tb = 29
Substituting the value of tb from equation b) into equation a):
ca + (229 - cb) = 164
ca = 164 - 229 + cb
ca = cb - 65
d) Considering that Dealership B sold half as many trucks as Dealership A, we can write the equation:
tb = 0.5 * ta
We can substitute this equation into equation b):
cb + 0.5 * ta = 229
Substituting the value of ta from equation a) into equation b):
cb + 0.5 * (ca + tb) = 229
cb + 0.5 * (cb - 65 + tb) = 229
Simplifying the equation:
1.5 * cb + 0.5 * tb = 229
1.5 * cb + 0.5 * (229 - cb) = 229
Simplifying further:
1.5 * cb + 0.5 * 229 - 0.5 * cb = 229
cb + 0.5 * 229 = 229
Solving this equation gives us cb = 35.
Therefore, Dealership A sold 35 trucks.
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A company owns two dealerships, both of which sell cars and trucks. Dealership A sells a total of 164 cars and trucks. Dealership B sells twice as many cars and half as many trucks as Dealership A, and sells a total of 229 cars and trucks.
(4 points)
a) An equation for the total cars and trucks for Dealership A:
b) An equation for the total cars and trucks for Dealership B:
c) How many cars did Dealership A sell?
d) Considering that Dealership B sold half as many trucks as Dealership A, how many trucks did Dealership B sell?
1 answer