# HSPT Math : Problem Solving

## Example Questions

### Example Question #61 : Problem Solving

Explanation:

Multiplying an algebraic fraction is the same as multiplying fractions. Just multiply the numerators and the denominators and simplify.

To simply, divide the numerator and the denominator by the greatest common factor of  and , which is .

### Example Question #62 : Problem Solving

Explanation:

To simplify divide the numerator and the denominator by the Greatest Common Factor, which is .

(when you are dividing, subtract the exponents)

### Example Question #63 : Problem Solving

Explanation:

To divide fractions, you multiply by the reciprocal (flip the denominator and multiply instead.  \

So the problem now looks like

.

Then you multiply across,

and

.

.

### Example Question #1 : Percentages

The price of a suit after a 20% employee discount is $240.00. What is the original price? Possible Answers: Correct answer: Explanation: Deducting a 20% discount is the same as charging 80% of the price, so$240.00 is 80% of the original price, which we call . Just solve this equation:

Explanation:

Multiply the price of the groceries before tax - $154.92 - by the decimal equivalent of 9% , which is 0.09. Round this tax to the nearest hundredth (cents), then add to the price of the groceries. Tax: Price after tax: ### Example Question #7 : Percentage Susan has a coupon for 10% off any one item at her favorite department store. There is also a storewide sale of 50% off all purchases. If Susan wants to by a shirt originally priced at$42, how much will she pay?

$20.00$21.00

$16.50$37.80

$18.90 Correct answer:$18.90

Explanation:

The storewide sale discounts the shirt by 50%:

Susan also has the 10% off coupon, so she's really paying 90% of the cost of the shirt:

### Example Question #5 : Percentages

Exactly  of the plants in a garden are tomato plants.  Which of the following could be the total number of plants in the garden?

Explanation:

The total number of plants has to be divisible by 3.  Of the answer choices, the only one that is divisible by 3 is 18.  You can check this because numbers that are divisible have the sum of their digits also divisible by 3. For example,

which is divisible by 3, so 18 is divisible by 3.