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The sum of two numbers is 184. If one-third of one exceeds one-seventh of the other by 8, find the smaller number
- a)92
- b)84
- c)72
- d)76
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
The sum of two numbers is 184. If one-third of one exceeds one-seventh...
Given:
The sum of two numbers = 184
Calculation:
Let the numbers be x and (184 − x)
According to the question,
x × (1/3) - (184 − x)/7 = 8
⇒ (7x - 552 + 3x)/21 = 8
⇒ 7x - 552 + 3x = 8 × 21
⇒ 10x = 168 + 552
⇒ x = 720/10 = 72
One number = 72
Other number = 184 − x = 184 - 72 = 112
∴ The smaller number is 72.
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The sum of two numbers is 184. If one-third of one exceeds one-seventh...
To solve this problem, let's assign variables to the two numbers. Let's call the larger number x and the smaller number y. We are given two pieces of information:
1) The sum of the two numbers is 184: x + y = 184
2) One-third of one number exceeds one-seventh of the other by 8: (1/3)x - (1/7)y = 8
We can solve this system of equations using substitution or elimination method. Let's use the substitution method.
Substituting the value of x from the first equation into the second equation, we get:
(1/3)(184 - y) - (1/7)y = 8
Multiplying through by 21 to eliminate the fractions, we get:
7(184 - y) - 3y = 168
Distributing, we have:
1288 - 7y - 3y = 168
Combining like terms, we get:
-10y = -1120
Dividing by -10, we get:
y = 112
So the smaller number is 112.
To verify this answer, we can substitute the value of y back into the first equation:
x + 112 = 184
x = 184 - 112
x = 72
So the larger number is 72.
Therefore, the correct answer is option C) 72.
1) The sum of the two numbers is 184: x + y = 184
2) One-third of one number exceeds one-seventh of the other by 8: (1/3)x - (1/7)y = 8
We can solve this system of equations using substitution or elimination method. Let's use the substitution method.
Substituting the value of x from the first equation into the second equation, we get:
(1/3)(184 - y) - (1/7)y = 8
Multiplying through by 21 to eliminate the fractions, we get:
7(184 - y) - 3y = 168
Distributing, we have:
1288 - 7y - 3y = 168
Combining like terms, we get:
-10y = -1120
Dividing by -10, we get:
y = 112
So the smaller number is 112.
To verify this answer, we can substitute the value of y back into the first equation:
x + 112 = 184
x = 184 - 112
x = 72
So the larger number is 72.
Therefore, the correct answer is option C) 72.
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