HSPT Math : How to solve two-step equations

Study concepts, example questions & explanations for HSPT Math

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Example Questions

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Example Question #1 : How To Solve Two Step Equations

Let  be the temperature expressed in degrees Celsius. Then the equivalent temperature  in degrees Fahrenheit can be calculated using the formula:

What is  expressed in degrees Fahrenheit?

Possible Answers:

Correct answer:

Explanation:

Example Question #1 : Solve Word Problems Leading To Equations: Ccss.Math.Content.7.Ee.B.4a

Let be the temperature expressed in degrees Fahrenheit. Then the equivalent temperature  in degrees Celsius can be calculated using the formula:

What is  expressed in degrees Celsius (to the nearest degree)?

Possible Answers:

Correct answer:

Explanation:

, which rounds to 

Example Question #3 : How To Solve Two Step Equations

On average, 1 in 50 apples that grow in an orchard will not be harvested. Of those, half will rot on the ground. If 500 apples are growing in an orchard, how many will rot on the ground?

Possible Answers:

Correct answer:

Explanation:

If there are 500 apples and 1 in 50 will remain unharvested, then we can find the number of unharvested apples by multiplying. 

10 apples will remain unharvested. Of those, half will rot on the ground. Multiply to find how many apples rot on the ground.

5 apples will rot on the ground.

Example Question #1 : How To Solve Two Step Equations

Billy is at the store purchasing flowers for his mother, his grandmother, and his friend. He finds roses on sale by the half dozen (6), tulips selling by the dozen (12), and daisies selling groups of 18. 

Billy wants to have the same number of flowers in each bouquet, so that he is able to give everyone the same number of each flower. How many bundles of roses, tulips, and daisies will he have to buy so he has the same amount of each? (Please answer by roses, tulips, then daisies.)

Possible Answers:

Correct answer:

Explanation:

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). 

Example Question #4 : How To Solve Two Step Equations

Erin is making thirty shirts for her upcoming family reunion. At the reunion she is selling each shirt for $18 apiece. If each shirt cost her $10 apiece to make, how much profit does she make if she only sells 25 shirts at the reunion?

Possible Answers:

Correct answer:

Explanation:

This problem involves two seperate multiplication problems. Erin will make $450 at the reunion but supplies cost her $300 to make the shirts. So her profit is $150.

Example Question #51 : Algebraic Fractions

Solve for .

Possible Answers:

Correct answer:

Explanation:

Cross multiply.

Dsitribute.

Solve for .

Example Question #2 : Solve Word Problems Leading To Equations: Ccss.Math.Content.7.Ee.B.4a

Write as an equation: 

"Ten added to the product of a number and three is equal to twice the number."

Possible Answers:

Correct answer:

Explanation:

Let  represent the unknown quantity.

The first expression:

"The product of a number and three" is three times this number, or 

"Ten added to the product" is

The second expression:

"Twice the number" is two times the number, or

.

The desired equation is therefore

.

Example Question #3 : Solve Word Problems Leading To Equations: Ccss.Math.Content.7.Ee.B.4a

Write as an equation: 

Five-sevenths of the difference of a number and nine is equal to forty.

Possible Answers:

Correct answer:

Explanation:

"The difference of a number and nine" is the result of a subtraction of the two, so we write this as

"Five-sevenths of" this difference is the product of  and this, or

This is equal to forty, so write the equation as

Example Question #4 : Solve Word Problems Leading To Equations: Ccss.Math.Content.7.Ee.B.4a

Write as an equation:

Twice the sum of a number and ten is equal to the difference of the number and one half.

Possible Answers:

Correct answer:

Explanation:

Let  represent the unknown number.

"The sum of a number and ten" is the expression . "Twice" this sum is two times this expression, or

.

"The difference of the number and one half" is a subtraction of the two, or

Set these equal, and the desired equation is

Example Question #2 : How To Solve Two Step Equations

Axes 4

In the above diagram, which of the four points is the -intercept of the line of the equation  ?

Possible Answers:

Correct answer:

Explanation:

The -coordinate of the -intercept of the line of an equation can be found by setting  and solving for :

 

The -intercept is the point , which is three units down from the origin. This is the point marked  in the diagram.

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