Problem 1 :
The sum of two consecutive even integers is ninety-four. Find the numbers.
Solution:
Let the two consecutive even integers be x and x + 2.
x + x + 2 = 94
2x + 2 = 94
2x = 92
x = 46
x + 2 = 46 + 2
= 48
So, the numbers are 46 and 48.
Problem 2 :
One hundred sixty-two guests attended a banquet. Three servers provided their beverages. The first server helped three times as many people as the second server and the third server helped twice as many people as the first server. How many guests did each server help?
Solution:
Assuming that the second server helped x guests. So the first server helped 3x guests, and the third server helped 6x guests.
x + 3x + 6x = 162
10x = 162
x = 16.2
3x = 3(16.2) = 48.6
6x = 6(16.2) = 97.2
So, the first server helped 48.6 guests, the second server helped 16.2 guests and the third server helped 97.2 guests.
Problem 3 :
The sum of three numbers is fifty-eight. The second number is four more than the first number and the third number is eight more than the second number. What are the numbers?
Solution:
The first number is x.
The second number is x + 4.
The third number is x + 4 + 8.
x + x + 4 + x + 4 + 8 = 58
3x + 16 = 58
3x = 58 - 16
3x = 42
x = 14
So, the first number = 14
Second number = x + 4 = 14 + 4 = 18
Third number = x + 4 + 8 = 14 + 4 + 8 = 26.
Problem 4 :
Two case workers share an office. The first case worker has fifteen active cases. The second case worker has twice the number of active cases. How many active cases does the office have?
Solution:
Let f = Number of cases the first caseworker has
t = total number of cases
t = 15 + 2f
t = 15 + 2(15)
= 15 + 30
t = 45 active cases
Problem 5 :
Nine times a number decreases by five is equal to forty-nine. What is the number?
Solution:
Let the number be x.
9x - 5 = 49
9x = 54
x = 6
So, the number is 6.
Problem 6 :
The sum of two consecutive integers is one hundred twenty-three. Find the two numbers.
Solution:
Let the two consecutive integers be x and x + 1.
x + x + 1 = 123
2x + 1 = 123
2x = 122
x = 61
x + 1 = 61 + 1
= 62
So, the two numbers are 61 and 62.
Problem 7 :
A college has two depositional systems classes with a total of two hundred thirty-seven students. One class has forty-five more students than the other class. How many students are in each class?
Solution:
Let class 1 be x students.
Then class 2 be x + 45 students.
x + x + 45 = 237
2x = 237 - 45
2x = 192
x = 96
x + 45 = 96 + 45 = 141
So, class 1 = 96 students
class 2 = 141 students.
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