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.

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 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.

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

First, find the ratio of nabs to nibs. We know that 1 nib is equal to 6 nubs. We also know that 2 nubs is equal to 3 nabs:

We can multiply both sides of the second equation by 3:

Now we can combine our two equations:

Our question asks for the number of nabs in 5 nibs. We know from the equation above that 1 nib is equal to 9 nabs. Multiply both sides by 5 to find how many nabs are equal to 5 nibs.

Our final answer is 45.

DO NOT pick 4 days, which would be the middle number between Bob and Gary's rates of 3 and 5 days respectively. The middle rate is the answer that students always want to pick, so the SAT will provide it as an answer to trick you!

Let's think about this intuitively before we actually solve it, so hopefully you won't be tempted to pick a trick answer ever again! Bob can build the house in 3 days if he works by himself, so with someone else helping him, it has to take less than 3 days to build the house! This will always be true. Never pick the middle rate on a combined rates problem like this! 

Now let's look at the problem computationally. Bob can build a house in 3 days, so he builds 1/3 of a house in 1 day. Similarly, Gary can build a house in 5 days, so he builds 1/5 of a house in 1 day. Then together they build 1/3 + 1/5 = 5/15 + 3/15 = 8/15 of the house in 1 day.

Now, just as we did to see how much house Gary and Bob can build separately in one day, we can take the reciprocal of 8/15 to see how many days it takes them to build a house together. (When we took the reciprocal for Bob, 3 days/1 house = 1/3 house per day.) The reciprocal of 8/15 is 15/8, so they took 15/8 days to build the house together. 15/8 days is almost 2 days, which seems like a reasonable answer. Make sure your answer choices make sense when you are solving word problems!

Take the total distance travelled (600 miles) and divide it by the total time travelled (6.5 hrs + 5.5 hrs = 12 hours) = 50 miles/hour 

Call the cars “Car A” and “Car B”.

The least common multiple for the travel time of Car A and Car B is 120. We get the LCM by factoring. Car A’s travel time gives us 3 * 2 * 5; Car B’s time gives us 2 * 2 * 2 * 5.  The smallest number that accommodates all factors of both travel times is 2 * 2 * 2 * 3 * 5, or 120. There are 60 minutes in an hour, so 120 minutes equals two hours. Two hours after 1:00pm is 3:00pm.

If Jon is driving at 10 feet per second he covers 10 * 60 feet in one minute (600 ft/min). In order to determine how far he travels in thirty minutes we must multiply 10 * 60 * 30 feet in 30 minutes.

There are 60 seconds in a minute and 60 minutes in an hour, therefore 3600 seconds in an hour. The arrow will travel 3600x10= 36,000 meters in an hour.