Catalina went on a game show and won their biggest prize! Catalina loves a good adventure, so she spent 3/4 of her prize money on a trip into space. She then spent 2/3 of her remaining money on training to climb Mount Everest. Finally, she donated the last remaining $100,000 to wildlife conservation.
How much money did Catalina win?
Need a hint?
Start by drawing a long, skinny rectangle to represent Catalina’s total prize money. Next divide your rectangle into four equal parts and shade in three of these parts. The shaded area represents the money she spent on the trip to space. The non-shaded part represents her remaining money.
Now, what would 2/3 of the remaining money look like on your rectangle? We recommend using a different colour to shade in the part she spent training for Everest.
Next ask: what did Catalina do with the remaining, non-shaded fraction of the rectangle?
Catalina won $1,200,000!
This problem uses lots of fractions. We’ll show you a quick way to solve it at the end but first we’ll work through a visual solution.
Start by drawing a long, skinny rectangle to represent Catalina’s total prize money. Next, follow along with the story and divide your rectangle into 4 equal parts. Then, you can shade in three of these parts to represent the space trip that cost 3/4 of Catalina’s total prize.
The non-shaded fourth of the rectangle is the money Catalina has left over after going to space. We know from the story that she uses 2/3 of this remaining money on training for Everest. So, divide the non-shaded portion into 3 equal parts. Next, use a different coloured pencil to shade in two of these parts to represent the cost of training for Everest.
We know that the last remaining non-shaded portion of the rectangle is equal to $100,000, Catalina’s wildlife donation. Now, we can work backwards to find the total prize money.
First, looking at our drawing, we can see that the Everest training cost exactly twice the amount donated, or $200,000. This means that the money remaining after the space trip is exactly 3 times the amount donated, or $300,000.
Second, we know from the story that the money remaining after the space trip is 1/4 of the total prize money, so Catalina must have won 4 times $300,000, which is $1,200,000.
This hints at a faster way to calculate the prize. Start by asking what fraction of the whole is the $100,000 wildlife donation? Well, it’s 1/3 of a 1/4, which multiplied together makes 1/12. (Use your drawing to convince yourself that the white portion fits exactly 12 times in your big rectangle.) This means $100,000 is 1/12 of the total prize money. Multiplying $100,000 by 12 gives us $1,200,000.