Solving Problems with Equivalent Ratios 05:33 minutes

Video Transcript

Transcript Solving Problems with Equivalent Ratios

Today we're visiting Paul's plant shop. Paul loves and cares for all his plants, but he has a particular affinity for his Dionaea muscipula, aka, his venus fly trap. This is because his venus fly trap, affectionately named Deon, wave hello, Deon, is a little plant with dreams of being a Broadway star. To give Deon the best care possible, Paul needs to solve problems with equivalent ratios. Deon, like all venus fly traps, needs a specific amount of light each day. 1 hour of light to 2 hours of darkness is the ideal ratio for Deon. We can represent this visually with a tape diagram that shows the parts of the ratio. Notice the one rectangle of light to two rectangles of darkness. With the tape diagram the ratio always remains the same. Therefore, using equivalent ratios, we can find out the number of hours of light that Deon needs per day. We all know there are 24 hours in a day, so during a 24-hour period, how long should Deon be exposed to light and how long should he spend in darkness? To find this solution, we divide the total hours, 24, by the total number of rectangles in the tape diagram. In this case, 3. Therefore, each rectangle represents 8 hours. This shows that, each day, Deon needs 8 hours of light and 16 hours of darkness. Wow! Looks like that sunlight has been good for Deon. To keep growing strong he needs some really good soil. Using a tape diagram, we can represent the soil mixture ideal for venus fly traps. Deon's soil should contain 5 parts peat moss, 3 parts silica sand, and 2 parts perlite. We need to know how much of each part of the soil will fit in Deon's 20-gallon flower pot. To solve we should count the total number of rectangles. There are 10 total rectangles. Dividing we see that each rectangle represents 2 gallons. Looks like we need 10 gallons of peat moss, 6 gallons of silica sand, and 4 gallons of perlite to fit the 20 gallon flower pot. Only the best for Deon! What nutrients Deon doesn't get through light and soil, he makes up for by trapping insects. For every 3 flies Deon catches, he eats 7 ants. This fall, Deon ate 48 more ants than flies. How many of each insect did he eat? This problem is a little bit different because we don't know how many insects Deon ate in total, but don't worry, we'll figure it out! We know that Deon ate 48 MORE ants than flies. The tape diagram for ants is 4 rectangles longer than the tape diagram for flies. So, these 4 more rectangles must represent the 48 MORE ants! To find the value of each rectangle, we divide the 48 by 4, and find that each rectangle equals 12 insects. Which means Deon ate 84 ants and 36 flies this fall. Is that right? Let's check. 84 minus 36 is 48 So there were 48 more ants. Too bad Deon's diet doesn't include breath mints. There are a few steps we should summarize about solving problems with equivalent ratios. First, create a tape diagram with given ratio. Tape diagrams help us visualize and solve ratios problems. Tape diagrams show the rectangles, or units, in a ratio and help us figure out their numeric value. If you know the overall total, like the 24 hours in the light example, divide this number by the total number of rectangles, to find the value of each rectangle.
This gives us the solution for each part of the ratio. We use the same steps of creating a tape diagram from given information. Except, if you know the difference between two quantities in a ratio, like the 48 more ants than flies, count how many MORE rectangles one tape diagram has compared to the other. Then, divide the difference between the quantities by the difference in the number of rectangles to find the value of each rectangle. This, again, gives us the solution for each part of the ratio. Paul has taken great care of Deon. Therefore, Deon has been able to develop quite an impressive vocal range! He's packed his bags and is off to Broadway.