Find a percentage of a quantity
Devise and use problem solving strategies (be systematic, work logically)
This problem explores percentages. Percentages are fractions that are used to express the whole divided into one hundred equal parts. One percent means one-hundredth part of a whole or unit, and the notation used is 1%. It is important that students develop a number sense for approaching percentage problems. To make reasonable estimates of percentage problems students need to be able to calculate 50%, 10% and 1% mentally. The ability to estimate answers, to have a sense of what the answer should be, and then use a calculator or pen and paper for exact answers is a powerful combination of techniques.
NASA has been trying to reduce the fuel consumption of its large rockets. Two companies, MOREGAS and JeTSAVE have come up with separate devices to save fuel. The MOREGAS invention will save 30% of fuel and JeTSAVE’s attachment will save 40%. One of the brains at NASA decides to couple the two devices. How much fuel can they save together?
- Introduce the problem – it is important that the students understand that the fuel savers are used consecutively.
- Brainstorm for ways to solve the problem.
- As the students work encourage them to think about how to estimate using percentages.
How could you estimate 30% of an amount? (less than 50% or ½, about 1/3)
- Encourage the students to write their solution as a letter to the manufacturers encouraging them to use both fuel saving devices.
- Share letters.
Extension to the problem
Could you use these devices to save 80% or more of the fuel?
What does it mean to save 30% of fuel? If 100 units of fuel are used per minute without the device, then only 70 units of fuel are used per minute with the device.
So, if you use the two devices, then of the 70 units that are used through the first invention, 60% of that, i.e. 42 units, are used in the second invention. There is a 58 unit or 58% saving.
As far as the extension problem goes it's first worth noting that the NASA brain wasn’t so brainy. If he had used two of the JeTSAVE devices he could have saved 64%.
60 units (60% gets through the first device) and then 60% of 60 = 36 units gets through the second device. This is a saving of 64%. Adding a third device would lead to a 78.4% saving. That’s almost 80%. So adding a fourth device should surely do it.
That raises several questions. Why didn’t JeTSAVE think of that for themselves and put four devices in a row? How much fuel can you save by putting a hundred devices together? Can you save 100% of the fuel? What’s the catch here? I guess it’s all to do with cost. Maybe four JeTSAVE devices are extremely expensive and will cost more than they save. Maybe they are too big and will make the rocket too heavy. What else might be happening?