NJSLA Mathematical Reasoning and Modeling 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?

Accepted Answer

150 + 8g = 550

Answer

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?

Accepted Answer

180 + 45b ≤ 2000

Answer

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?

Accepted Answer

The fixed monthly base fee, regardless of data usage.

Answer

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?

Accepted Answer

15 gallons

Answer

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?

Accepted Answer

0.80p - 10

Answer

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.

NJSLA Exam Practice Test

NJSLA Exam Practice Test

NJSLA Mathematical Reasoning and Modeling Questions and Answers