ratio problem solving with strip diagrams

Question

The ratio of Shauns cards to jessica cards is 5 to 3. After shaun gives jessica 15 of her cards, both girls have the same number of cards. How many cards do each have now?

 

The ratio of Shauns cards to jessica cards is 5 to 2. After shaun gives jessica 12 of her cards, both girls have the same number of cards. How many cards do each have now?

Answer 1

Lucky, I'll do the first part.

 

We start with 8 total parts. Shaun has 5 and Jessica has 3. We must have a total that is a multiple of 8, 5, and 3.

 

Let's start with 120. Then each part is 120/8 = 15 cards. Shaun has 5(15) = 75 and Jessica has 3(15) = 45. If we take 15 from 75, does it equal adding 15 to 45? Hey, it sure does.

 

They each now have 60 cards.

 

Another way to look at it is that giving away 15 cards puts us now at 4:4, right? The 15 cards are thusly one part, and 4(15) = 60 cards each.