In the mall's parking lot, there are three times as many cars as trucks. The number of motorcycles is twice the number of bikes and there are four times as many trucks as bikes. If the total number of vehicles is 285, how many cars are there?

1 Answer
Shiva Prakash M V
Feb 19, 2018

#"Hence, the number of cars is x_1=180"#

Explanation:

#"Let "x_1 "denote the number of cars"#
#"Let " x_2 "denote the number of trucks"#
#"Let "x_3 "denote the number of motorcycles"#
#"Let "x_4 "denote the number of bikes"#
#"Given:"#
#3x_1=x_2#
#2x_4=x_3#
#x_2=4x_4#
#x_1+x_2+x_3+x_4=285#
#x_1=?#

#3x_1=x_2#implies
#x_2=1/3x_1#

#x_2=4x_4#implies#x_4=1/4x_2=1/4xx1/3x_1#

#x_4=1/12x_1#

#2x_4=x_3#implies #x_3=2x_4=2xx1/12x_1#
#x_3=1/6x_1#

The sum of cars is 285

#x_1+x_2+x_3+x_4=285#

#x_1+1/3x_1+1/6x_1+1/12x_1=285#

#(1+1/3+1/6+1/12)x_1=285#

#(12/12+4/12+2/12+1/12)x_1=285#

#(12+4+2+1)/12x_1=285#

#19/12x_1=285#

#x_1=285/19xx12#

#x_1=15xx12#

#x_1=180#

#x+2=1/3x_1=1/3xx180=60#

#x_2=60#

#x_3=1/6x_1=1/6xx180=30#

#x_3=30#

#x_4=1/12x_1=1/12xx180=15#

#x_4=15#

#x_1+x_2+x_3+x_4=180+60+30+15#

#x_1+x_2+x_3+x_4=285#

Verified

#"Hence, the number of cars is x_1=180"#

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