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James has a collection of 20 miniature cars and trucks. Cars make up 40% of the collection. If James adds only cars to his collection, how many cars must he add to make the collection 75% cars?

 Jul 9, 2019
 #1
avatar
+1

Let the new cars to be added =C

0.75[C + 20] =0.40[20] + C

0.75C + 15  = 8 + C

0.75C - C = 8 - 15

- 0.25C  =  - 7

C = 7 / 0.25

C = 28 - New cars that must be added to his collection.

 Jul 9, 2019
 #2
avatar+23171 
+2

James has a collection of 20 miniature cars and trucks.
Cars make up 40% of the collection.
If James adds only cars to his collection,
how many cars must he add to make the collection 75% cars?

 

\(\begin{array}{|rcll|} \hline \mathbf{\text{cars }} &=& \mathbf{20\cdot40\ \%} \\\\ &=& \dfrac{20\cdot 40}{100} \\ &=& \mathbf{8} \\ \hline \end{array} \)

 

\(\begin{array}{|rcll|} \hline \mathbf{(20+x)\cdot75\ \%} &=& \mathbf{8+x} \\\\ (20+x)\cdot 0.75 &=& 8+x \\ 15+ 0.75x &=& 8+x \\ 7+ 0.75x &=& x \\ x- 0.75x &=& 7 \\ 0.25x &=& 7 \\ x &=& \dfrac{7}{0.25} \\ \mathbf{ x } &=& \mathbf{28} \\ \hline \end{array}\)

 

He must add 28 cars to make the collection 75% cars.

 

laugh

 Jul 9, 2019
 #3
avatar+103999 
+1

40% of the cars and trucks are cars  = .40 * 20  =  8

 

Let x be the number of cas he needs to add to  have 75% cars....so we have

 

[ 8 + x ] 

_______   =     .75          multiply  both sides by 20 + x

20 +  x

 

8 + x  =  .75  [ 20 + x ]

 

8 + x  = 15 + .75x    subtract .75x, 8 from both sides

 

.25x = 7        divide both sides by .25

 

x  = 28

 

So....he needs to add 28 cars to have 75% cars

 

 

cool cool cool

 Jul 9, 2019

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