LESSON 2.4

1. EVALUATING FORMULAS

1.1. Definition of a Formula - an equation that describes how two or more variables are related

1.2. EXAMPLE 1: The number of gallons of gasoline you put in your car is found using the equation c/p = n where c = the total cost, p = the price per gallon, and n = number of gallons. How many gallons of gas can you purchase for $51.00 if gas costs $4.25 per gallon?

1.2.1. C = 51.00, P = 4.25, n = (51.00/4.25) n = 12 gallons

1.3. EXAMPLE 2: The formula S = P - 0.25P gives the sale price S of an item originally costing P dollars that was reduced by 25%. Find the sale price of a pair of jeans that originally cost $40.

1.3.1. S = P - 0.25P, S = 40 - 0.25(40), S=40 - 10, S=30

1.4. EXAMPLE 3: Find the number of yards of fencing needed to enclose a garden that is 10.5 yards long (l) and 4.25 yards wide (w). Use the equation P = 2l + 2w

1.4.1. P=2L+2W, P=2(10.5) + 2(4.25) , P = 21 + 8.5, P = 29.5

2. SOLVING FORMULAS FOR A VARIABLE

2.1. Solve for a variable - to isolate the variable with a coefficient

2.2. EXAMPLE 1: Solve the equation 3X + 2Y = 6 SOLVE FOR Y

2.2.1. 3X + 2Y = 6, 2Y = 6 - 3X, Y = (6 - 3X)/2

2.3. EXAMPLE 2: Solve the equation P=2L + 2W. Solve for w

2.3.1. P= 2L+2W, P-2L=2W, (P-2L)/2=W

2.4. EXAMPLE 3: Solve the simple interest formula I=Prt. Solve for t

2.4.1. I=Prt, I/Prt=t