Terminology
Fill in the Blank:
An ________ is a meaningful combination of numbers and letters called terms.
Expression
Delta reduced its round-trip ticket price from Portland to Boston by $140. The sale price was $401.90. What was the original price? (Round your answer to the nearest cent.)
Original price $541.90
P - 140 = 401.90
+ 140 = + 140
P = 541.90
Solve the unknown from the following equation:
7Y = 259
Y = 37
Solve the unknown from the following equation:
A + 340 = 860
A = 520
Fill in the Blank:
________ and ________ are terms of mathematical expressions.
Variables and Constants
A local Best Buy sells 8 times as many iPods as Sears. The difference between their sales is 490 iPods. How many iPods did each sell?
iPods: Best Buy: 560 Sears: 70
Explanation:
8I - I = 490
7I = 490
7I / 7 = 490 / 7
I = 70
8I = 560
Solve the unknown from the following equation:
P / 9 = 91
P = 819
Solve the unknown from the following equation:
Q − 65 = 860
Q = 925
The following definition applies to what Rule?
You can add the same quantity or number to both
sides of the equation and subtract the same quantity or number from both sides of the equation without
affecting the equality of the equation.
Equation Equality Rule
The number of discouraged unemployed workers rose to 506,200, 212212 times as many as in the previous year. How many discouraged unemployed workers were there in the previous year?
Discouraged unemployed workers: 202,480
Explanation:
2 1/2 D = 506,200
(2 1/2 D) / 2 1/2 = 5-6,200 / 2 1/2
D = 202,480
Find X in the following ratios and proportions:
24 / 3 = x / 46
X = 368
Explanation:
(46) 24 / 3 = x(46) / 46
X = 368
Solve the unknown from the following equation:
13Y − 18 = 86
Y = 8
What rule tells us that when equations contain parentheses (which indicates grouping together), you solve for the unknown by first multiplying each item inside the parentheses by the number or letter just outside the parentheses.
The Distributive Rule
David Role is an employee of Google. He budgets 1/7 of his salary for clothing. If David’s total clothing bill for the year is $12,000, what is his yearly salary?
Yearly salary $84,000
Explanation:
(1/7)S = $12,000
7(s/7) = $12,000 (7)
S = $84,000
A quality control group found 7 defects for every 1,250 units produced. If 8,750 units were produced, how many defects were there?
Defects: 49
Explanation:
7 / 1,250 = x / 8,750
(8,750)7 / 1,250 = x
49 = x
Solve the unknown from the following equation:
8x + 6 – 2 + x = 20 - 4x + 10
X = 2
What is the definition of the Multiple Processes Rule?
When solving for an unknown that involves more than one process, do the addition and subtraction before the multiplication and division.
A local Dominos sold a total of 1,600 small pizzas ($9) and pasta dinners ($13) during the Super Bowl. How many of each did Dominos sell if total sales were $15,600? Check your answer.
Pasta: 300 Pizza: 1,300
Solve the unknown from the following equation:
29(P − 34) = 464
P = 50
Solve the unknown from the following equation:
23(P − 28) = P + 364 - 40
P = 44