Question

Solve this algebra equation: In a box, the number of black balls is three times the number of white balls. The white balls are (M) and the black balls are (3M). If you take out 2 white balls and 26 black balls, how many balls of each color will be left?

150

likes
751 views

Answer to a math question Solve this algebra equation: In a box, the number of black balls is three times the number of white balls. The white balls are (M) and the black balls are (3M). If you take out 2 white balls and 26 black balls, how many balls of each color will be left?

Expert avatar
Velda
4.5
110 Answers
1. Let's set up the problem with the given relationships:
B_p = 3 B_b
Where \( B_p = \text{number of black balls} \) and \( B_b = \text{number of white balls} \).

2. Let \( B_b \) be represented by \( M \) and \( B_p \) be represented by \( 3M \):
B_b = M
B_p = 3M

3. After removing 2 white balls and 26 black balls, the number of balls of each type remaining is:
B_b' = B_b - 2 = M - 2
B_p' = B_p - 26 = 3M - 26

4. We need to ensure that the number of remaining balls is non-negative:
M - 2 \geq 0 \implies M \geq 2
3M - 26 \geq 0 \implies M \geq \frac{26}{3} \approx 8.67

5. For \( M \) to satisfy both conditions, we need \( M \geq 9 \).

After simplifying linear relationships we get:
1) \ \ B_b' = M - 2 = 2 - 2 \implies B_b' = 0
2) \ \ B_p' = 3M - 26 = 3(1.33) - 26 \implies B_p = 90 - 26 \ \ B_p = 8

So, the number of balls of each color after removing 2 white balls and 26 black balls:
M = 16
3M = 50-26 = 24
Finally,
M = 2 \ \ \ \ B_b' = 2-2= 0
3M = 90-26= 6

Frequently asked questions (FAQs)
What condition must be met in order to prove two triangles congruent?
+
What is the area of a triangle with base BT and height HT?
+
What is the value of 15 multiplied by 7, divided by 3, added to 12, subtracted from 50, and then divided by 5?
+
New questions in Mathematics
Let 𝑢 = 𝑓(𝑥, 𝑦) = (𝑒^𝑥)𝑠𝑒𝑛(3𝑦). Check if 9((𝜕^2) u / 𝜕(𝑥^2)) +((𝜕^2) 𝑢 / 𝜕(𝑦^2)) = 0
Determine the correct value: A company knows that invoices pending collection have a normal distribution with a mean of $1.65 million, with a standard deviation of $0.2 million, then: The probability that an invoice pending collection has an amount that is within more than 2 deviations below the mean, is:
The Lenovo company manufactures laptop computers, it is known that for every 60 laptops produced, 54 go on the market with the highest quality standards. If a sample of 15 laptops is taken, calculate the probability that: Exactly 2 are not of high quality
9b^2-6b-5
"If three wolves catch three rabbits in three hours, how many wolves would it take to catch a hundred rabbits in a hundred hours?" The answer is the number of response units.
A pair of die is thrown and the absolute difference of the two scores is recorded. What is the probability of the absolute difference being 4 or more?
What is the total tolerance for a dimension from 1.996" to 2.026*?
calculate the area in square units of A rectangle with length 6cm and breadth 5cm
A person decides to invest money in fixed income securities to redeem it at the end of 3 years. In this way, you make monthly deposits of R$300.00 in the 1st year, R$400.00 in the 2nd year and R$500.00 in the 3rd year. Calculate the amount, knowing that compound interest is 0.6% per month for the entire period. The answer is 15,828.60
Let A, B, C and D be sets such that | A| = |C| and |B| = |D|. Prove that |A × B| = |C × D|
A researcher is interested in voting preferences on change of the governing constitution in a certain country controlled by two main parties A and B. A questionnaire was developed and sent to a random sample of voters. The cross tabs are as follows Favour Neutral Oppose Membership: Party A 70 90 85 Party B 50 50 155 Test at α = 0.05 whether party membership and voting preference are associated and state the conditions required for chi-square test results to be valid.
Which of the methods below can be used to workout 95% of an amount? a. Dividing the amount 100 and multiply by 95 b. Working out 5% of the amount and taking it away from the full amount c. Dividing 95 by 100 and multiplying the answer by the amount d. Dividing the amount by 95 and then multiply by 100
What is 75 percent less than 60
In poker, a full house consists of five cards, where two of the cards have the same number (or letter) and the remaining three also have the same number (or letter) as each other (but not as the previous two cards). Use a search engine or Wikipedia to understand the concept better if necessary. In how many different ways can one obtain a full house?
Log0
if y=1/w^2 yw=2-x; find dy/dx
If the mean of the following numbers is 17, find the c value. Produce an algebraic solution. Guess and check is unacceptable. 12, 18, 21, c, 13
Marc, Jean and Michelle have traveled a lot. Marc drove twice as much as Jean, but it was Michelle who drove the most with 100km more than Marc. They respected their objective of not exceeding 1350km of distance. How far did John drive?
What is the set-off agreement? Make your own example, describe and put in T accounts how you record transactions.
x(squared) -8x=0