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The larger of two numbers exceeds twice the smaller number by 9. The sum of twice the larger and 5 times the smaller number is 74. If a is the smaller number, which equation below determines the correct value of a?
- a)5(2a + 9) + 2a = 74
- b)5(2a - 9) + 2a = 74
- c)(4a + 9) + 5a = 74
- d)2(2a + 9) + 5a = 74
- e)2(2a - 9) + 5a = 74
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
The larger of two numbers exceeds twice the smaller number by 9. The s...
To solve this problem, first convert the information given into its mathematical equivalent, as follows (use b to represent the larger number):
The larger of two numbers exceeds twice the smaller number by nine: b = 2a + 9
The sum of twice the larger and five times the smaller number is 74: 2b + 5a = 74
Now, simply substitute the value of b into the second equation in order to solve for a: 2(2a + 9) + 5a = 74
The larger of two numbers exceeds twice the smaller number by nine: b = 2a + 9
The sum of twice the larger and five times the smaller number is 74: 2b + 5a = 74
Now, simply substitute the value of b into the second equation in order to solve for a: 2(2a + 9) + 5a = 74
Community Answer
The larger of two numbers exceeds twice the smaller number by 9. The s...
To solve this problem, we need to translate the given information into mathematical equations and then solve for the smaller number.
Let's assume the larger number is 'L' and the smaller number is 'a'.
According to the given information:
1. The larger number exceeds twice the smaller number by 9:
L = 2a + 9
2. The sum of twice the larger number and 5 times the smaller number is 74:
2L + 5a = 74
So, we have two equations:
Equation 1: L = 2a + 9
Equation 2: 2L + 5a = 74
Now, let's solve these equations to find the value of 'a'.
Solving Equation 1 for L:
L = 2a + 9
Substituting this value of L in Equation 2:
2(2a + 9) + 5a = 74
Simplifying the equation:
4a + 18 + 5a = 74
9a + 18 = 74
9a = 74 - 18
9a = 56
a = 56/9
Therefore, the value of 'a' is 56/9.
Now, let's look at the options given:
a) 5(2a - 9) + 2a = 74
b) 5(2a - 9) + 2a = 74
c) (4a + 9) + 5a = 74
d) 2(2a - 9) + 5a = 74
e) 2(2a - 9) + 5a = 74
The correct equation is option 'd' because it represents the equation we derived from the given information. Therefore, the correct value of 'a' is 56/9.
Let's assume the larger number is 'L' and the smaller number is 'a'.
According to the given information:
1. The larger number exceeds twice the smaller number by 9:
L = 2a + 9
2. The sum of twice the larger number and 5 times the smaller number is 74:
2L + 5a = 74
So, we have two equations:
Equation 1: L = 2a + 9
Equation 2: 2L + 5a = 74
Now, let's solve these equations to find the value of 'a'.
Solving Equation 1 for L:
L = 2a + 9
Substituting this value of L in Equation 2:
2(2a + 9) + 5a = 74
Simplifying the equation:
4a + 18 + 5a = 74
9a + 18 = 74
9a = 74 - 18
9a = 56
a = 56/9
Therefore, the value of 'a' is 56/9.
Now, let's look at the options given:
a) 5(2a - 9) + 2a = 74
b) 5(2a - 9) + 2a = 74
c) (4a + 9) + 5a = 74
d) 2(2a - 9) + 5a = 74
e) 2(2a - 9) + 5a = 74
The correct equation is option 'd' because it represents the equation we derived from the given information. Therefore, the correct value of 'a' is 56/9.
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The larger of two numbers exceeds twice the smaller number by 9. The sum of twice the larger and 5 times the smaller number is 74. If a is the smaller number, which equation below determines the correct value of a?a)5(2a + 9) + 2a = 74b)5(2a - 9) + 2a = 74c)(4a + 9) + 5a = 74d)2(2a + 9) + 5a = 74e)2(2a - 9) + 5a = 74Correct answer is option 'D'. Can you explain this answer?
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The larger of two numbers exceeds twice the smaller number by 9. The sum of twice the larger and 5 times the smaller number is 74. If a is the smaller number, which equation below determines the correct value of a?a)5(2a + 9) + 2a = 74b)5(2a - 9) + 2a = 74c)(4a + 9) + 5a = 74d)2(2a + 9) + 5a = 74e)2(2a - 9) + 5a = 74Correct answer is option 'D'. Can you explain this answer? for ACT 2025 is part of ACT preparation. The Question and answers have been prepared according to the ACT exam syllabus. Information about The larger of two numbers exceeds twice the smaller number by 9. The sum of twice the larger and 5 times the smaller number is 74. If a is the smaller number, which equation below determines the correct value of a?a)5(2a + 9) + 2a = 74b)5(2a - 9) + 2a = 74c)(4a + 9) + 5a = 74d)2(2a + 9) + 5a = 74e)2(2a - 9) + 5a = 74Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for ACT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The larger of two numbers exceeds twice the smaller number by 9. The sum of twice the larger and 5 times the smaller number is 74. If a is the smaller number, which equation below determines the correct value of a?a)5(2a + 9) + 2a = 74b)5(2a - 9) + 2a = 74c)(4a + 9) + 5a = 74d)2(2a + 9) + 5a = 74e)2(2a - 9) + 5a = 74Correct answer is option 'D'. Can you explain this answer?.
The larger of two numbers exceeds twice the smaller number by 9. The sum of twice the larger and 5 times the smaller number is 74. If a is the smaller number, which equation below determines the correct value of a?a)5(2a + 9) + 2a = 74b)5(2a - 9) + 2a = 74c)(4a + 9) + 5a = 74d)2(2a + 9) + 5a = 74e)2(2a - 9) + 5a = 74Correct answer is option 'D'. Can you explain this answer? for ACT 2025 is part of ACT preparation. The Question and answers have been prepared according to the ACT exam syllabus. Information about The larger of two numbers exceeds twice the smaller number by 9. The sum of twice the larger and 5 times the smaller number is 74. If a is the smaller number, which equation below determines the correct value of a?a)5(2a + 9) + 2a = 74b)5(2a - 9) + 2a = 74c)(4a + 9) + 5a = 74d)2(2a + 9) + 5a = 74e)2(2a - 9) + 5a = 74Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for ACT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The larger of two numbers exceeds twice the smaller number by 9. The sum of twice the larger and 5 times the smaller number is 74. If a is the smaller number, which equation below determines the correct value of a?a)5(2a + 9) + 2a = 74b)5(2a - 9) + 2a = 74c)(4a + 9) + 5a = 74d)2(2a + 9) + 5a = 74e)2(2a - 9) + 5a = 74Correct answer is option 'D'. Can you explain this answer?.
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