a) An equation for the total cars and trucks for Dealership A:
x + y = 164
The equation represents the total cars (x) and trucks (y) sold by Dealership A.
b) An equation for the total cars and trucks for Dealership B:
2x + (1/2)y = 229
The equation represents that Dealership B sold twice as many cars (2x) and half as many trucks ((1/2)y) as Dealership A, totaling to 229 cars and trucks.
c) To find how many cars Dealership A sold, we can solve the equation x + y = 164. There are multiple methods to solve this, but let's use substitution:
We can assume that x is the number of cars sold, and y is the number of trucks sold.
From equation a), we can write x = 164 - y.
Substituting this value of x in equation b), we have:
2(164 - y) + (1/2)y = 229
328 - 2y + (1/2)y = 229
328 - 229 = (3/2)y
99 = (3/2)y
Multiplying both sides by 2/3, we get:
66 = y
Therefore, Dealership A sold 66 trucks.
To determine how many cars were sold by Dealership A, we can substitute the value of y (66) in equation a):
x + 66 = 164
x = 164 - 66
x = 98
Therefore, Dealership A sold 98 cars.
d) Since Dealership B sold half as many trucks as Dealership A, and Dealership A sold 66 trucks, Dealership B sold 66/2 = 33 trucks.
The answers would be:
c) How many cars did Dealership A sell?
Option: 98
d) Considering that Dealership B sold HALF as many trucks as Dealership A, how many trucks did Dealership B sell?
Option: 33
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.
a) An equation for the total cars and trucks for Dealership A:
options: x+y=164, x+y=229, x+y=393
b) An equation for the total cars and trucks for Dealership B:
options: 1/2x+2y=164, 2x+1/2y=229, 1/2x+1/2y=229
c) How many cars did Dealership A sell?
options: 66, 132, 196, 98
d) Considering that Dealership B sold HALF as many trucks as Dealership A, how many trucks did Dealership B sell?
options: 33, 66, 49, 98
1 answer