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

likes751 views

Velda

4.5

105 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

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 \( 3M \):

3. After removing 2 white balls and 26 black balls, the number of balls of each type remaining is:

4. We need to ensure that the number of remaining balls is non-negative:

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

After simplifying linear relationships we get:

So, the number of balls of each color after removing 2 white balls and 26 black balls:

Finally,

Frequently asked questions (FAQs)

What is the equation of the logarithmic function that passes through the points (1, 3) and (2, 6)?

+

What is the equation of an exponential function that passes through the point (2, 5) and has a y-intercept of 8?

+

Math question: What is the probability of rolling a 6 on a fair six-sided die? (P(event) = number of favorable outcomes / total outcomes)

+

New questions in Mathematics