WORKSHEET ON CONSTRUCTING MODELS FOR SAT

Problem 1 :

Last Saturday, Maya drove from her house to the bookstore, where she stayed for several hours before driving back home. Which of the following graphs could represent Maya's trip ?

Solution

Problem 2 :

At a movie theater, an adult ticket costs $10 and a bag of popcorn costs $6. If a group of adults bought tickets to a movie and 4 bags of popcorn, what expression could be used to determine how much in total the group spent, in dollars ?

(a)  10x + 6, where x is the number of adults

(b)  10x + 24, where x is the number of adults

(c)  16x, where x is the number of adults

(d)  6x + 10, where x is the number of bags of popcorn purchased.

Solution

Problem 3 :

On Friday, Janice read x pages every 30 minutes for 4 hours, and Kim read y pages every 15 minutes for 5 hours. Which of the following represents the total number of pages read by Janice and Kim on Friday ?

(a)  4x + 5y     (b)  8x + 20y     (c)  20x + 8y    (d)  120x + 75y

Solution

Problem 4 :

At the start of a semester, 150 students enroll in a course for which the regular tuition fee is $5, 400. The school finds that for every $200 discounts on the tuition fee for the course, the students enrollment increase by 9. Which of the following equation gives the student enrollment E when the tuition fee for the course is discounted by d dollars ?

(a)  E = 150 + 0.045 d        (b)  E = 150 + 9d

(c)  E = 150+0.045(5400 - d)    (d)  E = 150+9(5400 - 200d)

Solution

Problem 5 :

Jones climbed a mountain at the speed of 1 kilometer per hour and came down at the speed of 2 kilometer per hour. Which of the following could be the graph of the distance from the bottom of the mountain as a function of time ?

Solution

Problem 6 :

Kevin has collected m coins. Ellie has collected half as many as Kevin, but 5 more than Robert. In terms of m, how many coins has Robert collected ?

(a)  2m - 5    (b) (m/2) + 5     (c)  2m + 5    (d)  (m/2) - 5

Solution

Problem 7 :

A clothing company sells its flagship winter jacket all year round. The table above shows the quantity demanded when the price of the jacket is $320 and when it is $360. Assuming the quantity demanded decrease at a constant rate with respect to price, which of the following linear functions Q best models the quantity demanded when the price of the jacket p in dollars ?

(a)  Q(p) = 93600 - 235p     (b)  Q(p) = 93600 - 260p

(c)  Q(p) = 93600 - 235(p - 320)

(d)  Q(p) = 93600 - 260(p - 320)

Solution

Problem 8 :

A movie rental service charges $15 as a monthly subscription fee and $3 per movie rented. If Alex rents x movies per month from this service, which of the following expression gives the total amount in dollars, he spends on movie rentals in one year ?

(a) 12(18x)   (b)  15 + 12(3x)

(c)  12(15) + 3x   (d) 12 (15 + 3x)

Solution

Problem 9 :

A car has an estimated initial value of $65000. Once the car is sold, its value decreases at a constant rate of $2300 per year. Which of the following equations best approximated the value V in dollars, of the car t years after it is sold, for 0 ≤ t ≤ 28 ?

(a)  V = 65000 + 2800t    (b)  V = 65000 - 2800t

(c)  V = 65000 + 2300t   (d)  V = 65000 - 2300t

Solution

Problem 10 :

A grocery store uses crates to store a total of 36a apples and 24w watermelons. Each crate can be used to store either 12 apples or 6 watermelons. Which of the following expression gives the total number of crates the grocery store uses to store apples and watermelons.

(a) 3a + 4w    (b)  4a + 3w    (c) 1/4a + 1/3w    (d)  1/3a + 1/4w

Solution