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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?
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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
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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.
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Directions:Read the passages and choose the best answer to each question.PassageA researcher has conducted two experiments to test the rate of pinecone production in the Pinus palustris Miller (a type of pine tre e).Experiment 1P. palustris Miller seeds were collected from 5 different populations (A1, A2, A3, A4, A5) each of which was from a different site (S1, S2, S3, S4, S5).The seeds were grown under controlled conditions in a greenhouse. 300 of these seedlings from each population were chosen at random. Each set of seedlings was divided into 30 groups with 10 seedlings in each group.The seedlings were planted in marked cylindrical containers which were then placed at each of the 5 sites. Figure 1 shows the procedure for A1.Table 1 shows the number of pinecones that were produced on each tree.The researchers also collected data on the root structure of the trees. From the information they collected they came up with the following formula relating the root structure in inches to the number of pinecones produced: number of pinecones = 0.037 + 0.147 (root thickness) Statistical analysis indicated that this equation was accurate.Experiment 2P. palustris Miller seeds were collected and grown in the same manner as in Experiment 1. When the seeds had grown into seedlings, 150 containers were prepared with 5 A1 seedlings and 5 seedlings from either A2, A3, A4 or A5. Seven containers for each of the 4 combinations were planted at each site.Table 2 shows how many pinecones were produced on each A1 plant.Q.In Experiment 1, A1 trees produced the largest number of pinecones at which of the following sites?

Directions:Read the passages and choose the best answer to each question.PassageA researcher has conducted two experiments to test the rate of pinecone production in the Pinus palustris Miller (a type of pine tre e).Experiment 1P. palustris Miller seeds were collected from 5 different populations (A1, A2, A3, A4, A5) each of which was from a different site (S1, S2, S3, S4, S5).The seeds were grown under controlled conditions in a greenhouse. 300 of these seedlings from each population were chosen at random. Each set of seedlings was divided into 30 groups with 10 seedlings in each group.The seedlings were planted in marked cylindrical containers which were then placed at each of the 5 sites. Figure 1 shows the procedure for A1.Table 1 shows the number of pinecones that were produced on each tree.The researchers also collected data on the root structure of the trees. From the information they collected they came up with the following formula relating the root structure in inches to the number of pinecones produced: number of pinecones = 0.037 + 0.147 (root thickness) Statistical analysis indicated that this equation was accurate.Experiment 2P. palustris Miller seeds were collected and grown in the same manner as in Experiment 1. When the seeds had grown into seedlings, 150 containers were prepared with 5 A1 seedlings and 5 seedlings from either A2, A3, A4 or A5. Seven containers for each of the 4 combinations were planted at each site.Table 2 shows how many pinecones were produced on each A1 plant.Q.A student wanted to produce the greatest number of pinecones from 6 A1 trees, using the procedures from Experiment 2. Which plants and site should the A1 trees be combined with to achieve the desired results?

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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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