SOLUTION: Hello, Question: The ratio of the number of toy cars to the number of toy trains in a shop was 2:3. When the shopkeeper bought 30 toy cars, the ratio of the number of toy cars

Algebra ->  Proportions  -> Lessons -> SOLUTION: Hello, Question: The ratio of the number of toy cars to the number of toy trains in a shop was 2:3. When the shopkeeper bought 30 toy cars, the ratio of the number of toy cars       Log On


   

Question 1162830: Hello,
Question:
The ratio of the number of toy cars to the number of toy trains in a shop was 2:3. When the shopkeeper bought 30 toy cars, the ratio of the number of toy cars to toy trains became 3:4. How many toy trains were there in the shop.
How would I go about setting up this problem and solving.
Thanks in advance.
Found 2 solutions by Boreal, solver91311:
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
2x/3x=2/3 x is the number of multiples, which is the same for each. We just don't know how many multiples, only that there is a single value for x in this store.
(2x+30)/3x=3/4
cross-multiply
9x=8x+120
x=120
so started with 240 cars and 360 trains
got 30 cars and now has 270 cars and 360 trains, and that is a 3:4 ratio (divide both by 90)

Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


Let represent the number of cars and represent the number of trains at the beginning.

Then we know that which is the same as:



After the purchase of the 30 cars, the situation changed to:



Which is to say:



Solve the 2X2 system for


John

My calculator said it, I believe it, that settles it