NJSLA Mathematical Reasoning and Modeling Questions and Answers — Questions and Answers
Question 1: A community center rents its main hall for a flat fee of $150 plus an additional $8 per guest. A school has a budget of exactly $550 for an awards banquet. Which equation can be used to determine the maximum number of guests, `g`, that can attend?
- 150g + 8 = 550
- 150 + 8g = 550 (Correct answer)
- 150 + 8 = 550g
- (150 + 8)g = 550
Correct answer: 150 + 8g = 550
The total cost is modeled by the sum of the fixed fee ($150) and the variable cost, which is $8 multiplied by the number of guests (`g`). This total must equal the budget of $550. Therefore, the correct equation is 150 + 8g = 550.
Question 2: An elevator has a maximum weight capacity of 2,000 pounds. A delivery person who weighs 180 pounds is using the elevator to transport identical boxes that each weigh 45 pounds. Which of the following inequalities correctly models the number of boxes, `b`, the delivery person can safely take in one trip?
- 45b - 180 ≤ 2000
- 180b + 45 ≤ 2000
- 180 + 45b > 2000
- 180 + 45b ≤ 2000 (Correct answer)
Correct answer: 180 + 45b ≤ 2000
The total weight in the elevator is the sum of the delivery person's weight (180 pounds) and the total weight of the boxes (45 pounds per box times `b` boxes). This combined weight, represented as 180 + 45b, must be less than or equal to (≤) the maximum capacity of 2,000 pounds.
Question 3: The monthly cost, `C`, of a cell phone plan is modeled by the equation `C = 0.15d + 40`, where `d` represents the amount of data used in gigabytes (GB). What does the number 40 represent in this equation?
- The cost for each gigabyte of data.
- The total number of gigabytes included in the plan.
- The fixed monthly base fee, regardless of data usage. (Correct answer)
- The maximum possible monthly charge.
Correct answer: The fixed monthly base fee, regardless of data usage.
In the linear model y = mx + b, 'b' represents the y-intercept, or the value of y when x is zero. In this context, if data usage `d` is 0, the cost `C` is $40. This represents the constant base fee that is charged every month even if no data is used.
Question 4: A recipe for a specific shade of paint requires mixing 3 parts blue paint with 5 parts yellow paint. A painter needs to make a total of 24 gallons of this paint. How many gallons of yellow paint does the painter need?
- 8 gallons
- 9 gallons
- 15 gallons (Correct answer)
- 19 gallons
Correct answer: 15 gallons
The total ratio is 3 + 5 = 8 parts. To find the value of one part, divide the total volume by the total number of parts: 24 gallons / 8 parts = 3 gallons per part. Since the recipe requires 5 parts of yellow paint, multiply the value of one part by 5: 3 gallons/part * 5 parts = 15 gallons of yellow paint.
Question 5: A store is having a sale where everything is 20% off the original price, `p`. A customer also has a coupon for an additional $10 off the sale price. Which of the following expressions correctly represents the final price the customer will pay?
- 0.20p - 10
- p - 0.20 - 10
- 0.80(p - 10)
- 0.80p - 10 (Correct answer)
Correct answer: 0.80p - 10
A 20% discount means the customer pays 80% of the original price. This is calculated as 0.80 * p. After this discount is applied, the $10 coupon is subtracted from that new sale price. This sequence of operations is correctly represented by the expression 0.80p - 10.
Question 6: A rectangular garden has a length that is 4 feet longer than its width, `w`. The perimeter of the garden is 56 feet. What is the area of the garden in square feet?
- 192 sq ft (Correct answer)
- 180 sq ft
- 168 sq ft
- 560 sq ft
Correct answer: 192 sq ft
Let `w` be the width. The length is `w + 4`. The formula for perimeter is P = 2(length + width). Substitute the values: 56 = 2((w + 4) + w). Simplify to 56 = 2(2w + 4), then 56 = 4w + 8. Solving for w gives 48 = 4w, so w = 12 feet. The length is w + 4 = 16 feet. The area is length × width, which is 16 ft × 12 ft = 192 sq ft.
NJSLA Mathematical Reasoning and Modeling Questions and Answers
A community center rents its main hall for a flat fee of $150 plus an additional $8 per guest.
A school has a budget of exactly $550 for an awards banquet.
Which equation can be used to determine the maximum number of guests, `g`, that can attend?