How to do other word problems - HSPT Math

Assume there are x pennies. Hence the number of nickels is 70-x.

Now you have to set up an equation for the dollar value of the pennies and nickels which will be x+5(70-x)=150.

Now solving for x results in x=50 (number of pennies). Hence the number of nickels will be 70-50=20.

We can find the prime factorization of a number by dividing 48 into smaller numbers.

48=2times 24

2 is prime

24=2times 12

2 is prime

12=2times 6

2 is prime

6=2times 3

Both 2 and 3 are prime.

So we have four 2's and one 3. Multiply these numbers to get 48.

One easy way to find the least common multiple is to take the largest of the numbers given to you, and find its multiples.

8: 8, 16, 24, 32, 40, 48...

Now start with 8, and see if any of these numbers is divisible by 6. The first number that is divisible by 6 is the least common multiple of 6 and 8.

8: No

16: No

24: Yes

24 is the least common multiple of 6 and 8.

Convert each fraction to a mixed number.

$\frac{16}{5}$=3$\frac{1}{5}$

$\frac{50}{7}$=7$\frac{1}{7}$

So how many whole numbers are between 3$\frac{1}{5}$ and 7$\frac{1}{7}$?

4, 5, 6, and 7 would fall between these two numbers. 3 would not. So there are 4 total whole numbers between them.

If Sarah borrowed 48 books and returned half of them, she now has

If she then borrowed 9 more, she added 9 to the 24 she had so now she has 33.

If Elaine wants to give 2 slices of pizza to 14 children, then she needs slices of pizza or 28 slices. 28 slices divided by the number of slice per pizza (8) will give you how many pizzas she needs.

.

In order to ensure she has enough pizza, she needs to round up so she needs to order 4 pizzas.

In two years, each person will be 2 years older. Since there are 3 of them, their ages will be years more, so we add 6 to the original total of 29

This is an arithmetic progression. Therefore you must add or subtract a number to the number before it to arrive at the next number. We must find the difference between each number and apply it to the final number to find the next number in the series.

To start, take the second number and subtract the first number.

In this case it yields

Then take the third number and subtract the second number which results in

If the resulting number is the same you now know the difference between each number in the sequence and can apply the difference to each resulting number.

In this case the difference is

So we take the final number and add the difference to it to result with

This is a conversion question.

There are 12 inches in a foot.

When multiplying monomials with the same base, you add the powers of each monomial together.

So in this case

Yielding an answer of

This tests your knowledge of scientific notation.

To solve you must move the decimal places to the right to the power of the ten.

In this case you must move the decimal place to the right 7 spaces from its original spot.

The solution is

This is a combination question.

To find the total number of sandwiches using only one ingredient we create three spaces for each ingredient and place each number of possible ingredients into each space.

We then multiply each number in each space together to find the answer

To answer this question we must first divide the original number by the number following it to get

Once we have this number we then square root it to find the answer

Absolute values are always positive so the absolute value of a negative number is just the number without the minus sign.

In this case the answer is

This is an arithmetic progression. Therefore you must add or subtract a number to the number before it to arrive at the next number.

We must first find the difference between each number.

To start, take the second number and subtract the first number

In this case it yields .

Then take the third number and subtract the second number which results in

If the resulting number is the same you now know the difference between each number in the sequence and can apply the difference to each break in the arithmetic sequence.

Again the difference is .

So we take the final number and add the difference to it resulting with

"2 pints in a quart, 4 quarts in a gallon"

To get the prime factorization of a number we must factor it in the most reduced version of prime numbers that multiplied together produce the number.

Prime numbers are numbers that are only divisible by themselves and 1. 1,2,3,5,7. . .

In this example we first divide the number by because its 3 and odd number which gives us

We now know that 3 is at least one of the prime factors.

Then we divide the result by 3 again to get

We then combine all of the prime numbers to get the answer of .

If we have a right angle triangle and a value for two of the three side lengths use the Pythagorean Theorem to solve for the length of the third side.

The two side lengths that meet to form the right angle are labeled and which are interchangeable for each side length. The long side connecting them is labeled and is known as the hypotenuse.

The Pythagorean Theorem states .

Take 3 and 4 and plug them into the equation as and to yield

First square the numbers .

After squaring the numbers add them together

Once you have the sum, take the square root of both sides

After calculating our answer is .

This is a geometric progression. Therefore you must multiply or divide a number by the number before it to arrive at the next number.

We must first find the ratio between each number.

To start, take the second number and divide the first number yielding

Then take the third number and divide the second number which results in

If the resulting number is the same you now know the ratio between each number in the sequence and can apply the ratio to each resulting number.

In this case the number is .

So we then take the final number and multiply it by 3 we received to get the answer of .