Concept explainers
(a)
Write an equation to represent the situation.
(a)
Answer to Problem 83PFA
Explanation of Solution
Given:
At a camp site in July, 120 families stayed for three or more days. The 120 families represent three − eighths of all the families who stayed at the campsite in July.
Concept Used:
The 120 families represent three − eighths of all the families who stayed at the campsite in July.
Let t = the total number of families
Three − eighths of all the families =
The 120 families represent three − eighths of all the families:
Calculation:
Equation:
Thus, the equation represent the situation is
(b)
Find the number of families stayed at the campsite.
(b)
Answer to Problem 83PFA
Option C is correct.
Explanation of Solution
Given:
At a camp site in July, 120 families stayed for three or more days. The 120 families represent three − eighths of all the families who stayed at the campsite in July.
Concept Used:
The 120 families represent three − eighths of all the families who stayed at the campsite in July.
Let t = the total number of families
Three − eighths of all the families =
The 120 families represent three − eighths of all the families:
Calculation:
Equation:
Solve fort = total number of family member.
Total number of family member is 320. Option C is correct.
Thus, total number of family member is 320. Option C is correct.
(c)
Write an equation to represent this situation.
(c)
Answer to Problem 83PFA
Explanation of Solution
Given:
In August, 120 families stayed for three more days and represent 40% of all the families who stayed at the campsite in August.
Let t = the total number of families.
Concept Used:
Let t = the total number of families.
120 families stayed for three more days and represent 40% of all the families who stayed at the campsite in August.
Convert the condition given in the question into algebraic equation.
Let t = the total number of families.
40% of all the families =
Total number of families stayed in August = 120 families.
Equation:
Calculation:
Equation:
Thus, the equation represent the situation is
(d)
Find the number of families stayed at the campsite in August?
(d)
Answer to Problem 83PFA
300
Explanation of Solution
Given:
In August, 120 families stayed for three more days and represent 40% of all the families who stayed at the campsite in August.
Let t = the total number of families.
Concept Used:
120 families stayed for three more days and represent 40% of all the families who stayed at the campsite in August.
Convert the condition given in the question into algebraic equation.
Let t = the total number of families.
40% of all the families =
Total number of families stayed in August = 120 families.
Equation:
Calculation:
Equation:
Solve for t = the total number of families.
The coefficient of t is
The reciprocal of the coefficient of t is
The total number of families stayed in August = 300
Thus, the total number of families in August is 300.
(e)
Describe how you could solve the equation from part C by using multiplication.
(e)
Answer to Problem 83PFA
Multiply each side by the reciprocal of the coefficient of t
Explanation of Solution
Given:
In August, 120 families stayed for three more days and represent 40% of all the families who stayed at the campsite in August.
Let t = the total number of families.
Concept Used:
120 families stayed for three more days and represent 40% of all the families who stayed at the campsite in August.
Convert the condition given in the question into algebraic equation.
Let t = the total number of families.
40% of all the families =
Total number of families stayed in August = 120 families.
Equation:
Calculation:
Equation:
Solve for t = the total number of families.
The coefficient of t is
The reciprocal of the coefficient of t is
Step 1: We need to multiply each side by the reciprocal of the coefficient of t
Step 2: Simplify
Thus, multiply each side by the reciprocal of the coefficient of t
(f)
Find number of more families stayed at the campsite in July than in August.
(f)
Answer to Problem 83PFA
Explanation of Solution
Given:
At a camp site in July, 120 families stayed for three or more days. The 120 families represent three − eighths of all the families who stayed at the campsite in July. In August, 120 families stayed for three more days and represent 40% of all the families who stayed at the campsite in August.
Concept Used:
In July: Equation:
In August: Equation:
Calculation:
In July: Equation:
Solve fort = total number of family member.
Total number of family member in July is 320
In August: Equation:
Solve for t = the total number of families.
The coefficient of t is
The reciprocal of the coefficient of t is
The total number of families stayed in August = 300
The total number of families stayed in July = 320
The total number of families stayed in August = 300
In July
Thus, in July
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