DSAT extra practice Ch1 Lv2

A crate can hold 18 carrots or 12 avocados. Dylan bought two crates of carrots and three crates of avocados. All crates collectively weigh 6 kilograms. Let [math]x[/math] be the weight, in grams, of a carrot and [math]y[/math] be the weight, in grams, of an avocado. Supposing the carrots all weigh the same and the avocados all weigh the same, which of the following equations best represent this situation?

Erika and Ethan went out for lunch. Erika s course costs $[math]x[/math] and Ethan’s course costs $8 more than Erika s. If they split the bill evenly and both paid a 20% tip, which of the following expressions represents the amount of money that Ian spent?

The factory manager claims that the net weight of a jar of strawberry jam is [math]280\pm10[/math]% grams. Let [math]x[/math] be the net weight of a jar of strawberry jam. If the manager s statement is true, which expression represents the range of [math]x[/math]?

The museum is open for 8 hours on weekdays. On weekends, it is open for [math]x[/math] extra hours. If the museum is closed on Tuesday every week, which expression represents the total number of hours the museum is open throughout the entire week?

Ashley’s laptop has a storage space of 512 GB. The last time she checked, there was still 182 GB of space on her laptop. Since Ashley loves to watch Korean dramas, she downloads three episodes every day. If [math]x[/math] represents the number of episodes of Korean dramas she downloaded and the average size of one episode is 1.2 GB, which of the following inequalities describes the restriction of [math]x[/math]?

$$a=\dfrac{2b^2}{2+c}$$Which of the following equations is equivalent to the equation above?

$$(a+b+c)(p+q)$$After expanding the expression above, how many terms will there be?

If [math]2x-7=13[/math], what is the value of [math]|-3(7-2x)+1|[/math]?

$$4(b-2x)=ax-12$$If the solution to the equation is all real numbers, what is the value of [math]a[/math] and [math]b[/math]?

If the reciprocal of the sum of twice a number [math]n[/math] and 3 is 0.125, what is the value of [math]n[/math]?

$$3^x\cdot9^{2x}=3^{240}$$What is the solution to the equation above?

$$(-2^x\cdot4^{-x})^2$$Which of the following expressions is equivalent to the expression above?

$$25\cdot2^x=5^y\cdot16$$If [math](x,y)=(a,b)[/math] are the solutions to the equation above, what is [math]a+b[/math]?

Easton, a doctor, drives a car from home to his clinic. The distance between his home and the clinic is 215 miles. If the average speed of Easton is 25 miles per half hour, how long will it take for Easton to get to the clinic?

There are 30 children in a room. If the ratio of the number of boys to the number of girls is 3 to 2, how many girls are there?

While building a sandcastle, Enzo found a piece of paper in a bottle. The paper is a treasure map. According to the scale, 4 centimeters on the map represents 50 meters. Suppose the distance between the location of the treasure and Enzo’s sandcastle is 26 centimeters on map. What is the actual distance between the treasure and his sandcastle?

A new type of incinerator can process 1,440 tons of waste per hour. How many kilograms of waste can this incinerator process per minute?

Ryan bought a pot to make corn soup. The pot can cook 4 gallon of corn soup every half hour. How many cups of corn soup can the pot cook per hour?

1 gallon [math]=[/math] 4 quarts

1quart [math]=[/math] 2 pint

1 pint [math]=[/math] 2 cups

Body mass index (BMI) is a value derived from the weight and height of a person. The formula is defined as the weight(kg) divided by the square of the height(m). If the BMI value of a person is over 25, then he/she is overweight. If Mr. Pig s height and weight are 5 feet and 108 kilograms respectively, what is his BMI?

1 foot [math]=[/math] 30 centimeters

Phillip dreams of having the naan he had during his trip to India last year again, so he decided to make it himself. According to the recipe, Phillip needs 3 cups of flour. Since Phillip s measuring cup is broken, he uses a spoon instead. If 1 cup of flour weighs 120 grams, and the spoon can hold half ounce of flour, how many spoons would Phillip need?

1 ounce [math]=[/math] 28.35 grams

As of June 2024, there are 486 boys and 520 girls in Happy School. In 2025, an average of 18 boys and [math]x[/math] girls leave from the school every year. If the number of boys start to exceed the number of boys after 7 years, what is [math]x[/math]?

If the inequalities [math]x-a<7[/math] has 11 positive integer solutions, what is the value of [math]a[/math]?

A triangle has a base of 6 cm. It has an area of at least 12 [math]\text{cm}^2[/math]. If the summation of the base and height is less than 13 cm and the height is an integer, what is the height of the triangle?

For every triangle, the summation of two sides must be greater than the third side. If a triangle has lengths 7 cm, 12 cm, and [math]x[/math] cm, which of the following numbers cannot be [math]x[/math]?

How many integers [math]n[/math] satisfy [math]|6-2n|\leq10[/math]?

$$|2x+1|+x=4$$What is the solution set of the equation above?