Engines make up 25% of Denise’s collection of 12 miniature train engines and boxcars. After Denise added new engines, her collection was 50% engines. How many engines did she add?

Question

3. Engines make up 25% of Denise’s collection of 12 miniature train engines and boxcars. After Denise added new engines, her collection was 50% engines. How many engines did she add?

Answer 1

25% of the collection of 12 is (25/100)12=12/4=3, so there are 3 engines in the set.

If x engines are added there will be x+3 engines in the set and there will be 12+x in the set as a whole.

So (x+3)/(12+x)=50/100=1/2,

Cross-multiply: 2(x+3)=12+x,

2x+6=12+x,

2x-x=12-6,

x=6 extra engines.

CHECK

There were 12 in the set, now there are 18 because of the 6 extra engines.

There were 3 engines in the set, now there are 9, and 9/18=1/2 which is 100/2=50%.