The Ratio of Blue Marbles to Green Marbles in the Box Is 13 to 24 How Many Marbles Are in the Box

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A bag contains 240 marbles that are either red, blue, or green. The ratio of red to blue to green marbles is 5 : 2 : 1. If one-third of the red marbles and two-thirds of the green marbles are removed, what fraction of the remaining marbles in the bag will be blue?

Explanation:

First, we need to figure out how many red, blue, and green marbles are in the bag before any are removed. Let 5x represent the number of red marbles. Because the marbles are in a ratio of 5 : 2 : 1, then if there are 5x red marbles, there are 2x blue, and 1x green marbles. If we add up all of the marbles, we will get the total number of marbles, which is 240.

5x + 2x + 1x = 240

8x = 240

x = 30

Because the number of red marbles is 5x, there are 5(30), or 150 red marbles. There are 2(30), or 60 blue marbles, and there are 1(30), or 30 green marbles.

So, the bag originally contains 150 red, 60 blue, and 30 green marbles. We are then told that one-third of the red marbles is removed. Because one-third of 150 is 50, there would be 100 red marbles remaining. Next, two-thirds of the green marbles are removed. Because (2/3)(30) = 20, there would be 10 green marbles left after 20 are removed.

To summarize, after the marbles are removed, there are 100 red, 60 blue, and 10 green marbles. The question asks us for the fraction of blue marbles in the bag after the marbles are removed. This means there would be 60 blue marbles out of the 170 left in the bag. The fraction of blue marbles would therefore be 60/170, which simplifies to 6/17.

The answer is 6/17.

Alan is twice as old as Betty.  He will be twice as old as Charlie in 10 years.  If Charlie is 2 years old, how old is Betty?

Explanation:

If Charlie is 2 years old now; in 10 years he will be 12 years old. At that point, Alan will be twice as old as Charlie. Twice 12 is 24. This means that Alan is currently 10 years younger than 24, or 14. Since Alan is currently twice as old as Betty, she must be half of 14, or 7.

The ratio of 10 to 14 is closest to what value?

Explanation:

Another way to express ratios is through division.  10 divided by 14 is approximate 0.71.

Tom wants to buy an aquarium.  He has found that that he needs one filter for the aquarium for every 40 creatures or plants he puts in the tank.  The fish he wants to get also requires special plants be present at 2 plants for every 5 fish.  These plants need 4 cleaning fish for every 3 plants in order to flourish.

If Tom is going to buy 3 filters, how many of the original fish he wanted will his aquarium support?

Correct answer:

Explanation:

3 filters can support a total of 120 creatures/plants.  The fish he wants need 2 plants for every 5 fish.  The plant needs 4 cleaning fish per 3 plants.  Thus for every 15 of the fish he wants, he needs 6 plants and 8 cleaning fish.

This gives us a total of 29 creatures.  We can complete this number 4 times, but then we are left with 4 spots open that the filters can support.

This is where the trick arises.  We can actually add one more fish in.  Since 1 plant supports up to 2.5 fish (2:5), and 2 cleaning fish support up to 1.5 plants, we can add 1 fish, 1 plant, and 2 cleaning fish to get a total of 120 creatures.  If we attempt to add 2 fish, then we must also add the 1 plant, but then we don't have enough space left to add the 2 cleaning fish necessary to support the remaining plant.

Thus Tom can buy at most 61 of the fish he originally wanted to get.

If the ratio of to is , what is the ratio of to ?

Correct answer:

Explanation:

You will get this problem wrong if you do not pay attention to what is being asked. The problem states that the ratio of m to n is .

Because the problem asks for the ratio of 3n to m, we have to multiply 13 * 3 = 39 to get 3n and 5 * 1 = 5 to get m (or 1m).

Then the requested ratio of 3n to m is 39 to 5 or.

In the reptile house at the zoo, the ratio of snakes to lizards is 3 to 5. After the zoo adds 15 more snakes to the exhibit, the ratio changes to 4 to 5. How many lizards are in the reptile house?

Explanation:

In order to maintain a proportion, each value in the ratio must be multiplied by the same value:

Before and after the snakes arrive, the number of lizards stays constant.

Before new snakes — Snakes : Lizards = 3x : 5x

After new snakes — Snakes : Lizards = 4x : 5x

Before the new snakes arrive, there are 3x snakes. After the 15 snakes are added, there are 4x snakes. Therefore, 3x + 15 = 4x. Solving for x gives x = 15.

There are 5x lizards, or 5(15) = 75 lizards.

If the ratio of q to r is 3:5 and the ratio of r to s is 10:7, what is the ratio of q to s?

Explanation:

Multiply the ratios. (q/r)(r/s)= q/s. (3/5) * (10/7)= 6:7.

A small company's workforce consists of store employees, store managers, and corporate managers in the ratio 10:3:1. How many employees are either corporate managers or store managers if the company has a total of employees?

Correct answer:

Explanation:

Let  be the number of store employees,  the number of store managers, and  the number of corporate managers.

, so the number of store employees is .

, so the number of store managers is .

, so the number of corporate managers is .

Therefore, the number of employees who are either store managers or corporate managers is .

The ratio of the number of financial employees who remained in the same role for 2 to 9 years to the number of construction employees who remained in the same role for 0 to 4 years is closest to which of the following?

Correct answer:

Explanation:

For this problem, we need to find the number of employees who fall into the categories described, keeping in mind that multiple portions of the pie chart must be accommodated for. Then, we can fit them into a ratio:

For the "2 to 9 years" portion of the financial industry, include

(0.2 + 0.18)(12,000,000) = 4,560,000 workers.

For the "0 to 4 years" portion of the construction industry, include

(0.15 + 0.2)(8,000,000) = 2,800,000 workers.

Now divide and simplify to find the ratio:

4,560,000/2,800,000 = 8/5.

Correct answer:

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