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)
Question: What is the vertex form of the quadratic function f(x) = -2x^2 + 4x + 3?
+
Find the maximum value of y = 5sin(3x) + 3cos(5x) on the interval [0, π].
+
Calculate the resultant vector when a vector of magnitude 15, pointing northeast, is added to a vector of magnitude 10, pointing directly east.
+
New questions in Mathematics
Let X be a discrete random variable with range {1, 3, 5} and whose probability function is f(x) = P(X = x). If it is known that P(X = 1) = 0.1 and P(X = 3) = 0.3. What is the value of P(X = 5)?
How do you think the company has increased or decreased its income?
x/20*100
Two events E and F are​ ________ if the occurrence of event E in a probability experiment does not affect the probability of event F.
4x-3y=24 and 5x-2y=9 solve by elimination
You are planning to buy a car worth $20,000. Which of the two deals described below would you choose, both with a 48-month term? (NB: estimate the monthly payment of each offer). i) the dealer offers to take 10% off the price, then lend you the balance at an annual percentage rate (APR) of 9%, monthly compounding. ii) the dealer offers to lend you $20,000 (i.e., no discount) at an APR of 3%, monthly compounding.
7/6-(-1/9)
The mean life of a television set is 119 months with a standard deviation of 13 months. If a sample of 67 televisions is randomly selected, what is the probability that the sample mean would be less than 121 months? Round your answer to four decimal places
Find the equation of the line perpendicular to −5𝑥−3𝑦+5=0 passing through the point (0,−2)
How many anagrams of the word SROMEC there that do not contain STROM, MOST, MOC or CEST as a subword? By subword is meant anything that is created by omitting some letters - for example, the word EMROSCT contains both MOC and MOST as subwords.
I want you to solve this problem as a grade sixth pupil in primary school: 8 Pigs ate 6 bags of fee in 20 days. How long will it take 10 pigs to eat 15 bags of feed eating at the same rate?
User The average height of Aranka, Böske, Cili, Delinke and Lili is 172 cm. We know that Aranka and Cili are both 172 cm tall. The sum of the heights of Böské and Delinke is 336 cm. How tall is Lili?
How to convert 45 kg into grams
The mass of 120 molecules of X2C4 is 9127.2 amu. Identify the unknown atom, X, by finding the atomic mass. The atomic mass of C is 12.01 amu/atom
A house located within the city limits has a current market value of $325,000 according to a recent appraisal. The assessed value from the last county wide tax valuation is $272,475. The tax rate is $0.36 per hundred for the county and $0.72 per hundred for the city. What is the total annual property tax liability on the property? $2340 $3510 $1962 $2943
A 20,000 kg school bus is moving at 30 km per hour on a straight road. At that moment, it applies the brakes until it comes to a complete stop after 15 seconds. Calculate the acceleration and the force acting on the body.
a coffee shop has 9 types of creamer and 11 types of sweetener. In how any ways can a person make their coffee?
Beren spent 60% of the money in her piggy bank, and Ceren spent 7% of the money in her piggy bank to buy a joint gift for Deren, totaling 90 TL. In the end, it was observed that the remaining amounts in Ceren and Beren's piggy banks were equal. Therefore, what was the total amount of money that Beren and Ceren had initially? A) 120 B) 130 C) 150 D) 160 E) 180
Solve the system of equations by the addition method. 0.01x-0.08y=-0.1 0.2x+0.6y=0.2
(3.1x10^3g^2)/(4.56x10^2g)