SAT Prep

If (x, y) satisfies the system of equations below, what is the value of y? -x + y = -3.5 x + 3y = 9.5

Hector used a tool called an auger to remove corn from a storage bin at a constant rate. The bin contained 24,000 bushels of corn when Hector began to use the auger. After 5 hours of using the auger, 19,350 bushels of corn remained in the bin. If the auger continues to remove corn at this rate, what is the total number of hours Hector will have been using the auger when 12,840 bushels of corn remain in the bin?

• 3

• 7

• 8

• 12

Tags

CCSS.6.RP.A.3B

An economist modeled the demand Q for a certain product as a linear function of the selling price P. The demand was 20,000 units when the selling price was $40 per unit, and the demand was 15,000 units when the selling price was $60 per unit. Based on the model, what is the demand, in units, when the selling price is $55 per unit?

• 16,250

• 16,500

• 16,750

• 17,500

The cost of renting a backhoe for up to 10 days is $270 for the first day and $135 for each additional day. Which of the following equations gives the cost y, in dollars, of renting the backhoe for x days, where x is a positive integer and x ≤ 10?

• y = 270x - 135

• y = 270x + 135

• y = 135x + 270

• y = 135x + 135

Tags

CCSS.5.OA.B.3

Adam’s school is a 20-minute walk or a 5-minute bus ride away from his house. The bus runs once every 30 minutes, and the number of minutes, w, that Adam waits for the bus varies between 0 and 30. Which of the following inequalities gives the values of w for which it would be faster for Adam to walk to school?

• w - 5 < 20

• w - 5 > 20

• w + 5 < 20

• w + 5 > 20

Tags

CCSS.6.NS.C.7C

Alan drives an average of 100 miles each week. His car can travel an average of 25 miles per gallon of gasoline. Alan would like to reduce his weekly expenditure on gasoline by $5. Assuming gasoline costs $4 per gallon, which equation can Alan use to determine how many fewer average miles, m, he should drive each week?

Tags

CCSS.7.EE.B.3

A laundry service is buying detergent and fabric softener from its supplier. The supplier will deliver no more than 300 pounds in a shipment. Each container of detergent weighs 7.35 pounds, and each container of fabric softener weighs 6.2 pounds. The service wants to buy at least twice as many containers of detergent as containers of fabric softener. Let d represent the number of containers of detergent, and let s represent the number of containers of fabric softener, where d and s are nonnegative integers. Which of the following systems of inequalities best represents this situation?

• 7.35d + 6.2s ≤ 300, d ≥ 2s

• 7.35d + 6.2s ≤ 300, 2d ≥ s

• 14.7d + 6.2s ≤ 300, d ≥ 2s

• 14.7d + 6.2s ≤ 300, 2d ≥ s

Tags

CCSS.7.EE.B.3

A local transit company sells a monthly pass for $95 that allows an unlimited number of trips of any length. Tickets for individual trips cost $1.50, $2.50, or $3.50, depending on the length of the trip. What is the minimum number of trips per month for which a monthly pass could cost less than purchasing individual tickets for trips?28

Mathematical Equivalence

ON

In the xy-plane, line k intersects the y-axis at the point (0, -6) and passes through the point (2, 2). If the point (20, w) lies on line k, what is the value of w?

Tags

CCSS.7.RP.A.2D

• 16.38

• 48.38

• 475.29

• 507.29