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There are 40  cars in a parking lot, all of which are 2-door or 4-door, and each car is either a compact car or an SUV. There are twice as many compact 4-door cars as compact 2-door cars, and three times as many 2-door SUVs as compact 2-door cars. If there are exactly as many compact 4-door cars as there are 4-door SUVs, then how many compact 2-door cars are in the parking lot?

 Dec 15, 2019
 #1
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+1

 x + 2x + 3x +2x = 40 and x =40 / 8 =5 compact 2-door cars in the parking lot.

 

40 Cars                    2-door                  4-door
Compact(C)               5                           10
SUV(S)                      15                          10
                               ---------                   --------
Totals                        20                            20

 Dec 15, 2019
 #2
avatar+109750 
+1

2* compact 2-door  = compact 4-door     (1)

3* compact 2-door  = SUV 2-door          (2)

compact 4-door = SUV 4 door                (3)

 

compact 2-door  + SUV 2-door  +  compact 4-door  + SUV 4-door  = 40       (4)

 

Sub (1), (2) and (3)  into (4)

Note that using  (1) and (3).....2compact 2-door = SUV 4-door....so.....

 

compact 2-door + 3compact 2-door + 2*compact 2-door + 2*compact 2-door  = 40

 

Simplifying....we have that

 

8 *compact 2-door  =40       divide both sides by  8

 

compact 2-door  =  40/8  =    5

 

Proof

There are  5 compact 2-door

There are 10 compact 4-door

There are 15 SUV 2-door

There are 10 SUV 4-door

 

 

cool cool cool

 Dec 15, 2019

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