Question

75 POINTS IF U GET THIS CORRECT!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! 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?

Answer 1

28 cars

Step-by-step explanation:

• cars + trucks = 20

Let "n" be the cars added in the collection

• cars : 20 * 40% = 8 cars

• trucks : 20 - 8 = 12 trucks

solve:

`\rightarrow \sf (8+n)/(20+n) =75\%`

`\rightarrow \sf {8+n} =(20+n)75\%`

`\rightarrow \sf {8+n} =15+0.75n`

`\rightarrow \sf {8-15} =0.75n-n`

`\rightarrow \sf -7 =0.25n`

`\rightarrow \sf n = 28`

Thus, he needs to add 28 cars in the collection to make the collection 75% cars.

Answer 2

28 cars

Step-by-step explanation:

Total number of cars and trucks = 20

Cars make up 40% of the collection

⇒ Number of cars = 40% of 20

= 0.4 x 20

= 8 cars

⇒ Number of trucks = total collection - number of cars

= 20 - 8

= 12 trucks

To calculate how many cars must be added to make the collection 75% cars, set up a ratio equation with x being the number of cars to be added:

(Added cars + existing cars) to total collection = 75%

⇒ x + 8 : x + 8 + 12 = 75 : 100

⇒ x + 8 : x + 20 = 75 : 100

`\sf \implies (x+8)/(x+20)=(75)/(100)`

⇒ 100(x + 8) = 75(x + 20)

⇒ 100x + 800 = 75x + 1500

⇒ 100x -75x = 1500 - 800

⇒ 25x = 700

⇒ x = 28

Therefore he would need to add 28 cars to his collection to make his collection 75% cars.

Check

Number of cars = 8 + 28 = 36

Number of trucks = 12

Total collection = 36 + 12 = 48

Number of cars / total collection = 36/48 = 0.75 = 75%