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?
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.
+26367 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.
+128475 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
