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Archy [21]
2 years ago
9

The ratio of red to blue marbles in a bag is 2:5. If there are 65 blue marbles in the bag, how many red marbles are there? Let x

represent the number of red marbles. Set up a proportion and cross multiply to solve.
Mathematics
1 answer:
hoa [83]2 years ago
8 0

Answer:

first get the total ratio; 2 + 5 = 7

so the fraction of blue marbles is 5/7

then assume the number of total marbles to be k

then use the expression;

5/7*k = 65

7*5/7 * k = 65*7

5k =455

5/5k = 455/5

k = 91

then calculate the number if red marbles from;

x = 2/7*91

x = 26

Therefore there are 26 red marbles.

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mrs_skeptik [129]

Answer:

The profit will be maximum on x = 250.

Step-by-step explanation:

From the given information:

Revenue = 1500x - x²

Cost = 1500 + 1000x

As we know that

Profit = Revenue - Cost ; Let say it equation 1

Then after putting the values of revenue and cost in equation 1 we have:

Profit = (1500x - x²) - (1500 + 1000x)

Profit = 1500x - x² - 1500 - 1000x

Profit = -x² + 500x - 1500

We know that at the max or min the slope of the graph formed by the profit function will be zero, therefore we find the slope of profit function by taking the first derrivative w.r.t. x as under:

d(Profit)/dx = d/dx(-x² + 500x - 1500)

d(Profit)/dx = -2x + 500

By putting the above slope equal to zero we get:

d(Profit)/dx = -2x + 500 = 0

-2x + 500 = 0

-2x = -500

x = 250

Therefore it is concluded that the profit will be maximum when x will be equal to 250.

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