b) An equation for the total cars and trucks for Dealership B: 2x + 0.5y = 300
c) To find the number of cars Dealership A sold, we can substitute the equation from part(a) into the equation from part (b):
2x + 0.5y = 300
2x + 0.5(225-x) = 300
2x + 112.5 - 0.5x = 300
1.5x = 187.5
x = 125
Dealership A sold 125 cars.
d) To find the number of trucks Dealership B sold, we can substitute the value of x that we found in part(c) into the equation from part(b):
2(125) + 0.5y = 300
250 + 0.5y = 300
0.5y = 50
y = 100
Dealership B sold 100 trucks.
Use your graphing calculator: Desmos Graphing Calculator A company owns two dealerships, both of which sell cars and trucks. Dealership A sells a total of 225 cars and trucks. Dealership B sells twice as many cars and half as many trucks as the Dealership A, and sells a total of 300 cars and trucks. (4 points) a) An equation for the total cars and trucks for Dealership A: x + y = 225 b) An equation for the total cars and trucks for Dealership B: c) How many cars did Dealership A sell? d) Given the fact that Dealership B sold half as many trucks as Dealership A, how many trucks did Dealership B sell?
7 answers
The sum of two numbers is 22. Three times one number increased by five is 35.(4 points) Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse. a) What are the equations you would use? Response area and Response area b) What are the two numbers? Response area and Response area
a) The equations we would use are:
x + y = 22 (Equation 1)
3x + 5 = 35 (Equation 2)
b) To solve the system of equations, we can use substitution or elimination method. Let's solve it using substitution method.
From Equation 1, we have: y = 22 - x
Substitute this value of y into Equation 2:
3x + 5 = 35
3x = 30
x = 10
Now substitute the value of x back into Equation 1 to find y:
10 + y = 22
y = 12
Therefore, the two numbers are 10 and 12.
x + y = 22 (Equation 1)
3x + 5 = 35 (Equation 2)
b) To solve the system of equations, we can use substitution or elimination method. Let's solve it using substitution method.
From Equation 1, we have: y = 22 - x
Substitute this value of y into Equation 2:
3x + 5 = 35
3x = 30
x = 10
Now substitute the value of x back into Equation 1 to find y:
10 + y = 22
y = 12
Therefore, the two numbers are 10 and 12.
Joelle currently has 18 rocks in her collection and gains 4 each week. Lewis currently has 30 rocks in his collection and gains 3 each week. Set up a system of equations to show how many rocks each has in their collection.(6 points) Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse. a) Joelle has y = Response areax + Response area b) Lewis has y = Response areax + Response area c) After how many weeks will Joelle and Lewis have the same number of rocks in their collections? Response area weeks d) How many rocks will Joelle and Lewis have when the amount of rocks in their collection is equal? They will each have Response area rocks in their collection.
a) Joelle has y = 4x + 18 (Equation 1)
b) Lewis has y = 3x + 30 (Equation 2)
c) To find after how many weeks Joelle and Lewis will have the same number of rocks, we can set Equation 1 equal to Equation 2 and solve for x:
4x + 18 = 3x + 30
Simplifying the equation:
x = 12
After 12 weeks, Joelle and Lewis will have the same number of rocks in their collections.
d) To find out how many rocks Joelle and Lewis will have when the amount of rocks in their collections is equal, substitute the value of x back into either Equation 1 or Equation 2:
Using Equation 1:
y = 4(12) + 18
y = 48 + 18
y = 66
Joelle and Lewis will each have 66 rocks in their collections when the amount of rocks is equal.
b) Lewis has y = 3x + 30 (Equation 2)
c) To find after how many weeks Joelle and Lewis will have the same number of rocks, we can set Equation 1 equal to Equation 2 and solve for x:
4x + 18 = 3x + 30
Simplifying the equation:
x = 12
After 12 weeks, Joelle and Lewis will have the same number of rocks in their collections.
d) To find out how many rocks Joelle and Lewis will have when the amount of rocks in their collections is equal, substitute the value of x back into either Equation 1 or Equation 2:
Using Equation 1:
y = 4(12) + 18
y = 48 + 18
y = 66
Joelle and Lewis will each have 66 rocks in their collections when the amount of rocks is equal.
Solve the system of equations 3x+2y=2 −2x+y=8 (1 point) Responses (-2, 4) (-2, 4) (14, -20) (14, -20) (-4, 2) (-4, 2) (4, -2)
To solve the system of equations:
3x + 2y = 2 (Equation 1)
-2x + y = 8 (Equation 2)
We can solve this system using the substitution or elimination method.
Let's use the elimination method:
Multiply Equation 2 by 2 to make the coefficients of x in both equations cancel each other out:
-4x + 2y = 16 (Equation 3)
Now, add Equation 1 and Equation 3 together:
(3x + 2y) + (-4x + 2y) = 2 + 16
-x + 4y = 18 (Equation 4)
Now we have a new equation, Equation 4.
Let's solve it for x:
-x + 4y = 18
x = 18 - 4y
Now substitute this value of x into Equation 1:
3(18 - 4y) + 2y = 2
54 - 12y + 2y = 2
-10y = -52
y = 5.2
Substitute the value of y back into Equation 2 to find x:
-2x + 5.2 = 8
-2x = 2.8
x = -1.4
Therefore, the solution to the system of equations is (x, y) = (-1.4, 5.2), which can be approximated as (-2, 4).
3x + 2y = 2 (Equation 1)
-2x + y = 8 (Equation 2)
We can solve this system using the substitution or elimination method.
Let's use the elimination method:
Multiply Equation 2 by 2 to make the coefficients of x in both equations cancel each other out:
-4x + 2y = 16 (Equation 3)
Now, add Equation 1 and Equation 3 together:
(3x + 2y) + (-4x + 2y) = 2 + 16
-x + 4y = 18 (Equation 4)
Now we have a new equation, Equation 4.
Let's solve it for x:
-x + 4y = 18
x = 18 - 4y
Now substitute this value of x into Equation 1:
3(18 - 4y) + 2y = 2
54 - 12y + 2y = 2
-10y = -52
y = 5.2
Substitute the value of y back into Equation 2 to find x:
-2x + 5.2 = 8
-2x = 2.8
x = -1.4
Therefore, the solution to the system of equations is (x, y) = (-1.4, 5.2), which can be approximated as (-2, 4).