Q: Sabina’s car has 50% better fuel efficiency (miles per gallon) than her old car. The new car uses diesel which is 20% more costly than the gas in her old car. On a percent basis, how much will she save on a long trip?
For this problem, we made up numbers to make the Math easier 🙂
We can use 10 miles per gallon for Sabina’s old car which would make the new one 15 mpg.
We can pick an easy number that plays nice with 10 and 15 like 30.
If she goes 30 miles on a trip, she will need 3 gallons with the old car but only 2 gallons with the new car.
Now we need a price for gas so we assumed $4.
If gas is $4/gallon but diesel is 20% more at $4.80 per gallon, she would have spent 3 x $4 = $12 with the old car but now spends only $9.60 for the new car (2 x $4.80).
She saved $2.40 on $12 which is a 20% savings.
Shout out to New York the Empire State aka the Regents State! The Regents is coming!
CC Algebra I is the most important Regents as s’s need at least 1 Math Regents to graduate and Alg I is so much more accessible than Geo or Alg II.
The best prep: Do Regents questions!!
There are certain questions that all and I mean ALL students should be able to answer correctly and get 2 points! Too often, students have not seen all the content and/or are not adept at the TI-83/4 calculator.
Make sure that you and your student(s), teacher(s) feel empowered to take the exam and learn Math in the process 🙂
Here is a link to the Bible of Algebra I (thanks to the jmap folks!)
If you prefer, you can call it an OED of Algebra I or the Primer of Algebra I.
The initial height means no time has passed and therefore t = 0.
The Regents offers this physics application of Math which is super easy to solve and learn!
When x = 0, in other words at 0 seconds, how high is the rocket?
You may not need a calculator to substitute in x = 0 🙂
Q: Two coins are flipped and you cannot see the outcome but are told that at least one is a head. What is the probability that the other coin also landed on heads?
This is a classic probability question. Once you know that one coin is a head, there are 3 possible outcomes for the two coins with at least one head.
Since you know that one is a heads, and there are 3 possible outcomes, the probability is 1/3.
Q: How many 6 digit numbers are there whose digits sum to 51?
There are 3 possible sets of 6 numbers: 999996 where the 6 can be the 1st, 2nd, 3rd, 4th, 5th, 6th place values making 6 6 digit numbers
3 9s and 3 8s which is the same probability as 3 boys and 3 girls with 6 children 3C6 = 20 6 digit numbers
and 4 9s with an 8 and a 7 with 30 possibilities
credit to Julia Robinson Mathematics Festival