How to find the solution to an equation - ISEE Middle Level Quantitative Reasoning

This is a least common multiple problem because we want to have the same number of each flower; meaning if I have 10 roses in each bouquet I should have 10 tulips and 10 daisies as well. In order to solve this problem we should break down the story problem. Let's look at the numbers we are having to work with: 6, 12, 18.

To do least common multiple we must look at the prime factors of each number and we can list them out. A factor is simply a number multiplied by a number to give us a product. A prime number is a number that contains only two factors, one of them being 1 and the other its own number.

So lets list the prime factors of 6, 12, and 18

(2 and 3 are both prime numbers, and factors of 6)

(2 x 2 = 4. 4x3=12 We have to say 2 x 2 because 4 is not a prime number).

Now we have the prime factors listed out for each of our numbers. Next is a fun trick. We must choose which number contains the most of each prime factor. In this case which number contains the most 2's? (12; because 12 has two 2 prime factors). Which number contains the most 3's? (18; because 18 has two 3 prime factors).

Our next step is to multiply the most of our prime factors so in this case:

36 is our least common multiple. So now what do you think we can do with this number? Well the 36 means that is the lowest number of flowers we need of each type in order to have an equal amount of each for the boquets.

Knowing this, if we need 36 roses, and we are able to buy 6 roses per bundle. We need 6 bundles of roses, because 36 divided by 6 is 6. If we get 12 tulips by the bundle, we take 36 divided by 12 to give us 3 bundles of tulips needed. Lastly we can buy 18 daisies per bundle, 36 divided by 18 gives us 2 bundles needed giving us our answers 6, 3, 2 (bundles of roses, tulips, and daisies).

First find the exponent value for each number:

Then divide accordingly. The answer is 128.

First, following order of operations, multiply:

Then, divide:

Multiply:

Answer:

First, solve the square root:

Then, solve the equation accordingly:

First, divide .

Then, calculate what time Angelina will arrive by adding 3 hours to 6:00.

The answer is 9:00 AM.

First, convert each fraction into an improper fraction. Then, change the operation to multiplication and flip the second fraction. Reduce and multiply.

Multiply:

Answer:

First, subtract 3 from both sides:

Now divide by 4 on both sides:

To solve:

First, solve both equations on each end, keeping the variable.

Then, subtract 15 from each side of the equation.

Finally, divide each side by 3 so that only the variable remains.

Cara finishes first. Ann and Bailey finish before Jill. If Jack finishes right before Bailey, then Jill finishes last.

Subtract 19, then divide by 7:

First multiply the original price by 30%.

Then subtract that amount from the original price.

The sale price is $84.00

First solve the parentheses.

Then solve from left to right since multiplication and division are interchangeable:

The answer is 20.

First, convert each mixed number into an improper fraction.

Then, reduce where possible and multiply.

Finally, convert your answer into a mixed-number fraction.

First, convert each mixed number into an improper fraction and flip the second fraction. Then, change the operation to multiplication:

Reduce where possible and multiply. Convert your answer into a mixed fraction.

First, combine the integers on the left side of the equation, and then do the same on the right:

Then subtract 16 from each side:

8 = 4a

Finally, divide both sides by 4 to isolate the variable:

First follow order of operations and solve on each side.

Then, subtract 40 from each side to leave only the variable:

Finally, divide both sides by 2.

The answer is

First solve with order of operations on each side:

Then subtract 15 from each side:

Finally, divide each side by 5:

The answer is 5.

Solve inside the parentheses first:

Follow order of operations to solve:

The answer is 21.