Set up the Equation
Sarah earns $12 per hour. Write an equation to represent how much money M she earns for H hours of work.
M = 12H
x + 5 = 12
x = 7
Rewrite for t
d = 4t
t = d/4
You earn $10 for every car you wash. Which is the independent variable: number of cars washed or money earned?
Cars Washed
The number that makes an equation true when substituted for a variable.
Solution.
A school charges $5 per ticket for a play. Write an equation that shows how much money T is made from selling n tickets.
T = 5n
y - 9 = 4
y = 13
Rewrite for s
A = s + 9
s = A - 9
You are selling cookies for a bake sale. Each cookie is sold for one dollar. What is the dependent quantity?
Total amount of money earned
The variable whose value depends on another variable.
Dependent Variable
Mike has 3 more than twice the number of baseball cards as John. Let m be Mike's cards and j be John's. Write an equation to represent the amount of cards each boy has.
m = 2j+ 3
a/6 = 3
a = 18
Rewrite for f:
C = f/5
f = 5C
A plant’s height increases each week. Identify the independent variable.
Time (weeks)
A mathematical sentence that shows two expressions are equal.
Equation
A rental car company charges a flat fee of $25 plus $0.20 per mile driven. Let C be the total cost for m miles.
C = 0.2m + 25
4t = 168
t = 42
Rewrite for x
y = x + 3.14
x = y - 3.14
A taxi fare (cost) is based on the number of miles driven. Which variable is dependent?
Total Cost (fare)
This states that if you add, subtract, multiply, or divide both sides of an equation by the same number, the equality stays true.
Properties of Equality
You are buying x apples that cost $0.75 each and y oranges that cost $0.50 each. Write an equation for the total cost C.
C = 0.75x + 0.50y
3(x+2) = 24
x = 6
Rewrite for w:
P = 2w + 2l
w = (P - 2l) / 2
The speed of a car (rate) affects how long it takes to reach a destination. Identify the independent and dependent variables.
Speed: Independent
Travel Time: Dependent
The process of undoing an operation to solve for a variable.
Inverse Operation