Discover the best answers at Westonci.ca, where experts share their insights and knowledge with you. Connect with a community of experts ready to provide precise solutions to your questions on our user-friendly Q&A platform. Explore comprehensive solutions to your questions from knowledgeable professionals across various fields on our platform.
Sagot :
Sure, let's solve the problem step-by-step.
We are given two pieces of information:
1. A is greater than B by 1/3 of the sum of A and B.
2. If B is increased by 40, it becomes greater than twice A by 10.
Let's denote [tex]\( A \)[/tex] and [tex]\( B \)[/tex] as the unknown values we need to find. We can set up the following equations based on the given information:
1. From the first statement, we have:
[tex]\[ A = B + \frac{1}{3}(A + B) \][/tex]
2. From the second statement, we have:
[tex]\[ B + 40 = 2A + 10 \][/tex]
We will solve these equations step-by-step.
### Step 1: Solve the first equation for [tex]\( A \)[/tex] in terms of [tex]\( B \)[/tex]
From the first statement:
[tex]\[ A = B + \frac{1}{3}(A + B) \][/tex]
Let's clear the fraction by multiplying through by 3:
[tex]\[ 3A = 3B + A + B \][/tex]
Combine the like terms:
[tex]\[ 3A = 4B + A \][/tex]
Now subtract [tex]\( A \)[/tex] from both sides to isolate [tex]\( A \)[/tex]:
[tex]\[ 2A = 4B \][/tex]
Divide both sides by 2:
[tex]\[ A = 2B \][/tex]
### Step 2: Substitute [tex]\( A = 2B \)[/tex] into the second equation
We have:
[tex]\[ B + 40 = 2A + 10 \][/tex]
Substitute [tex]\( A = 2B \)[/tex] into this equation:
[tex]\[ B + 40 = 2(2B) + 10 \][/tex]
Simplify:
[tex]\[ B + 40 = 4B + 10 \][/tex]
Subtract [tex]\( B \)[/tex] from both sides:
[tex]\[ 40 = 3B + 10 \][/tex]
Subtract 10 from both sides:
[tex]\[ 30 = 3B \][/tex]
Divide both sides by 3:
[tex]\[ B = 10 \][/tex]
### Step 3: Find [tex]\( A \)[/tex] using [tex]\( B \)[/tex]
We found that [tex]\( B = 10 \)[/tex]. Now use [tex]\( A = 2B \)[/tex]:
[tex]\[ A = 2 \cdot 10 = 20 \][/tex]
### Conclusion
Thus, the values of [tex]\( A \)[/tex] and [tex]\( B \)[/tex] are [tex]\( A = 20 \)[/tex] and [tex]\( B = 10 \)[/tex]. Therefore, the correct answer is:
(C) 20, 10
We are given two pieces of information:
1. A is greater than B by 1/3 of the sum of A and B.
2. If B is increased by 40, it becomes greater than twice A by 10.
Let's denote [tex]\( A \)[/tex] and [tex]\( B \)[/tex] as the unknown values we need to find. We can set up the following equations based on the given information:
1. From the first statement, we have:
[tex]\[ A = B + \frac{1}{3}(A + B) \][/tex]
2. From the second statement, we have:
[tex]\[ B + 40 = 2A + 10 \][/tex]
We will solve these equations step-by-step.
### Step 1: Solve the first equation for [tex]\( A \)[/tex] in terms of [tex]\( B \)[/tex]
From the first statement:
[tex]\[ A = B + \frac{1}{3}(A + B) \][/tex]
Let's clear the fraction by multiplying through by 3:
[tex]\[ 3A = 3B + A + B \][/tex]
Combine the like terms:
[tex]\[ 3A = 4B + A \][/tex]
Now subtract [tex]\( A \)[/tex] from both sides to isolate [tex]\( A \)[/tex]:
[tex]\[ 2A = 4B \][/tex]
Divide both sides by 2:
[tex]\[ A = 2B \][/tex]
### Step 2: Substitute [tex]\( A = 2B \)[/tex] into the second equation
We have:
[tex]\[ B + 40 = 2A + 10 \][/tex]
Substitute [tex]\( A = 2B \)[/tex] into this equation:
[tex]\[ B + 40 = 2(2B) + 10 \][/tex]
Simplify:
[tex]\[ B + 40 = 4B + 10 \][/tex]
Subtract [tex]\( B \)[/tex] from both sides:
[tex]\[ 40 = 3B + 10 \][/tex]
Subtract 10 from both sides:
[tex]\[ 30 = 3B \][/tex]
Divide both sides by 3:
[tex]\[ B = 10 \][/tex]
### Step 3: Find [tex]\( A \)[/tex] using [tex]\( B \)[/tex]
We found that [tex]\( B = 10 \)[/tex]. Now use [tex]\( A = 2B \)[/tex]:
[tex]\[ A = 2 \cdot 10 = 20 \][/tex]
### Conclusion
Thus, the values of [tex]\( A \)[/tex] and [tex]\( B \)[/tex] are [tex]\( A = 20 \)[/tex] and [tex]\( B = 10 \)[/tex]. Therefore, the correct answer is:
(C) 20, 10
Thanks for using our service. We aim to provide the most accurate answers for all your queries. Visit us again for more insights. We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. Westonci.ca is your trusted source for answers. Visit us again to find more information on diverse topics.