Remedial Math: Feb 24. 2014 Applying Equations 3.2 & 3.3

1.) 12 Cups of Coffee: 98% Water: x= actual coffee

12 * .98 is the same as .98 * 12, but I have trouble recognizing that. Commutative, either way. 

That is wrong because it is really the 2% we are looking for-   .02 * 12 = x               x=0.24

2.) 90mL of Alcohol: 12% alcohol: total capacity in bottle (aka x -what we are looking for.)

.12 * x = 90

How do we solve this: divide .12/.12 (which now become .12 even though it looks like twelves its not twelve I swear its point one two. 

.12/.12 * x= 90/.12 = 750 mL

3.) More Formulas: Quantit of Substance= Amount of Solution *Percent        See here: Q=Ar

Distance= rate * time        See: d=r(t)       Ex: 13 miles is our distance, rate is 2 miles because your getting pushed back by 3 miles, and time is unknown (x), so 13=2(x) How do we solve this: Get rid of x, so we divide. 13/2 = 2x/2 that right there cancels and we are left with 13/2 which is 6.5 hours. Final answer x= 6.5 hours. 

4.) Number * Variable = Number           like this: ax=b 

Dealing with percents: Of means Multiply, Is means Equal. Seen like this, Of: Multiplication, is: Equals

Percent * Base Amount = Amount Change

  • 289.99 * .06 = $17.40 that’s how much tax, now 289.99 + 17.40= 307. 39 that was the total price. 
  • Here’s another way: (1 + 0.6) * 289.99 = 307.39  that was: (1+percent) * Base Amount = New Amount 

A.) 70% of 330-   Equation:  330 * .7 = x   Multiply   x=231

B.) What is 27% of 14-  Equation:    .15/.15 * x = 24/.15    Divide    15/24= 160 Move the decimal over

C.) 15 % of what number is 24-  Equation   x * .27/.27 = 14/.27    Divide 27/140 = .51815   repeating Move the decimal x= 51.851%

D.) 30% of 90- Equation: Multiply   .3 * 90= 27    then Subtract    90 – 27 =  63. 

Another way: (100%-30%) * 90         70%* 90       .7 * 90 = 63

I = Prt (Interest = Principle * rate * time)  

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