Concept explainers
To find: the numbers based on the given description
Answer to Problem 12P
The smaller number is
Explanation of Solution
Given information: “The difference of two numbers is 9”, “Five times the smaller is 7 more than three times the larger”
Concept Involved:
Assign variable for the unknown that we need to find.
Use the keywords in the statement to rewrite the statement to meaningful math equation.
“is” means =
“more than” means +
“Difference” means -
“times” means ×
Solve the equation by getting the variable in one side of the equation and undoing whatever is done to it by performing reverse operation.
Calculation: Assign variable for the unknown that we need to find
Let x represents smaller number
Since the difference of two numbers is 9, the expression that represents the larger number is x more than 9.
Rewrite the statement “Five times the smaller is 7 more than three times the larger” in terms of x
5 times x is 7 more than 3 times
Use the keywords to write the statement “Five times the smaller is 7 more than three times the larger” as an equation
Distribute 5 in right side of the equation
In the process of getting x in one side of the equation subtract 3x on both sides
Combine like terms on both sides
Divide 2 on both sides of the equation
Simplify fraction on both sides of the equation
Substitute 17 for x in the expression
Conclusion:
The smaller number is
Chapter 3 Solutions
Algebra: Structure And Method, Book 1
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