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Ian had some toy cars and toy planes in two boxes A and B. At first, there were 12 toy cars and 20 toy planes in Box A while there were 28 toy cars and 40 toy planes in Box B. He transfered some toy cars from Box B to Box A and some toy planes from Box A to Box B. In the end, the ratio of the number of toy cars to the number of toy planes in Box A was 4:3 while the ratio of the number of toy cars to the number of toy planes in Box B was 1:2.

(a)    Find the number of toy planes in Box A in the end.

(b)    In the end, how many more toy cars were there in Box B than Box A?

 Sep 8, 2021
 #1
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(a)    Find the number of toy planes in Box A in the end.

(b)    In the end, how many more toy cars were there in Box B than Box A?

 

Hello RunningMan!

 

     A                                             B

12c+20p                                 28c+40p                     beginning

12c+20p+xc -yp                     28c+40p-xc+yp          

(12+x)c+(20-y)p                     (28-x)c+(40+y)p

(12+x):(20-y)=4:3                   (28-x):(40+y)=1:2        end

36+3x=80-4y                          56-2x=40+y               

 

\(y=-9-0.75x+20\\ y=16-2x\\ 16-2x=11-0.75x\\ -1.25x=-5\)

\(x=4\\ y=8\)                                         \(x=4\\ y=8\)

\((12+x)c+(20-y)p\\ (12+4)c+(20-8)p\\ \color{blue}16\ cars+12\ planes\)           \((28-x)c+(40+y)p\\ (28-4)c+(40+8)p\\ \color{blue}24\ cars+48\ planes\)

\(24\ cars-16\ cars=8\ cars\)

 

\((a)\ The\ number\ of\ {\color{blue}toy\ planes\ in\ Box\ A}\ in\ the\ end\ is\color{blue}\ 12. \)

 

\((b)\ {\color{blue}8\ cars\ more}\ toy\ cars\ were\ there\ \color{blue}in\ Box\ B\ than\ Box\ A.\)

laugh  !

 Oct 4, 2021
edited by asinus  Oct 4, 2021
edited by asinus  Oct 4, 2021

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