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)
Math question: How many different ways can 5 students be arranged in a line for a class photo?
+
What is the resulting vector when multiplying vector A by vector B?
+
Math question: What is the probability of drawing a red card from a standard deck of 52 playing cards?
+
New questions in Mathematics
I need .23 turned into a fraction
Using the integration by parts method, calculate the integral of [x².ln(1/x)]dx: x 4 /4 x³/6 x 4 /8 x³/3 x 4 /6
Which of the following is the product of multiplying twenty-seven and twenty-five hundredths by nine and twenty-seven hundredths?
A bird randomly chooses to land on 1 of 12 perches available in its aviary. Determine the Probability of it landing on a perch numbered 8 and then on a perch marked with a prime number; take into account that he never lands on the same perch in the sequence.
(5u + 6)-(3u+2)=
224 × (6÷8)
How long will it take for $900 to become $5000 at an annual rate of 11.15% compounded bimonthly?
Solve this mathematical problem if 3/5 of a roll of tape measures 2m. How long is the complete roll? Draw the diagram
Clara usually walks briskly to the farmers' market and it takes her 22 minutes. Today she walked leisurely and it took 61/2 minutes. How much more time than usual did she take to reach the market today?
4x + 8y = 5 2x + 4y = 10
You mix a powder drug with a 4.5ml of liquid to get a reconstituted solution with a concentration of 250mg/ml. The prescribers order is for 500 mg . You will give what ml of the reconstituted solution
A stunt man jumps horizontally from a building to the roof of a garage that is 2 meters lower. How fast does he need to be to land on the roof of the said garage that is 3 meters away from the building?
2)A tourist has 15 pairs of pants in his hotel room closet. Suppose 5 are blue and the rest are black. The tourist leaves his room twice a day. He takes a pair of pants and puts them on, the tourist leaves the first pair of pants in the closet again and takes another one and puts them on. What is the probability that the two pants chosen are black?
(2m+3)(4m+3)=0
At the dance there are 150 boys the rest are girls. If 65% are girls what is the total amount in the room
The volume of a cube decreases at a rate of 10 m3/s. Find the rate at which the side of the cube changes when the side of the cube is 2 m.
A popular cell phone family plan provides 1500 minutes. It charges 89.99/month for the first 2 lines and 9.99 for every line after that. Unlimited text messages for all phone lines costs $30.00/month, and Internet costs $10.00/month per phone line. If a family with a $200 monthly budget buys this plan and signs up for unlimited text messaging and Internet on each phone line, how many cell phone lines can they afford? Use an inequality to solve this problem. Graph your solution on the number line and explain the meaning of your graph in a sentence.
a coffee shop has 9 types of creamer and 11 types of sweetener. In how any ways can a person make their coffee?
Two trains leave stations 294 miles apart at the same time and travel toward each other. One train travels at 95 miles per hour while the other travels at 115 miles per hourHow long will it take for the two trains to meet?
Question 3 A square has a perimeter given by the algebraic expression 24x – 16. Write the algebraic expression that represents one of its sides.