MAT 1100 Quantitative Reasoning: Module 3 Lesson 3 Assignment 2

This document contains the complete solutions to Assignment 2 of Module 3, Lesson 3 in the MAT 1100 Quantitative Reasoning course. The assignment includes a variety of word problems focusing on solving systems of equations and applying these skills to real-world scenarios. The problems cover topics such as calculating ticket sales, determining the number of people who paid different prices at a ball game, finding the dimensions of a rectangle given its perimeter, solving mixture problems, and solving investment problems involving compound interest. Additional problems involve calculating the rate of the wind based on travel times and distances. Each solution is presented with clear, step-by-step explanations, including the setup of equations and the algebraic steps to arrive at the correct answer, making it a valuable resource for students to understand and learn the concepts.

MAT 1100 Quantitative Reasoning Module 3 Lesson 3 Assignment 2
Student Name:
Solve the problems.
1) Ron and Kathy are ticket-sellers at their class play, Ron handling student tickets that sell for $1.00 each and
Kathy selling adult tickets for $4.50 each. If their total income for 25 tickets was $74.00, how many did Ron
sell?
Solution: Suppose that Ron sales x ticket. Since the total number of tickets sold were 25. Then will be
the number of tickets sold by Kathy. Then according to the question
Simplify we get
Thus, Ron sold 11 tickets.
2) There were 32,000 people at a ball game in Los Angeles. The day's receipts were $276,000. How many
people paid $13.00 for reserved seats and how many paid $6.00 for general admission?
A) 20,000 paid $13 and 12,000 paid $6 B) 11,000 paid $13 and 21,000 paid $6
C) 21,000 paid $13 and 11,000 paid $6 D) 12,000 paid $13 and 20,000 paid $6
Solution: Suppose that x number of people paid $13.00 for reserved seats, then 32,000 – x will be the number
of people paid $6.00 for general admission. Then according to the question
Hence, 12,000 paid $13 and 32,000 – x = 32000 – 12000 = 20,000 paid $6.
Therefore, option (D) is correct.
3) The perimeter of a rectangle is 82 m. If the width were doubled and the length were increased by 23 m, the
perimeter would be 164 m. What are the length and width of the rectangle?
Solution: Suppose that the length and width of the rectangle l and b respectively. Then the perimeter will be

MAT 1100 Quantitative Reasoning Module 3 Lesson 3 Assignment 2
,
If the width were doubled and the length were increased by 23 m, the perimeter would be 164 m, this implies
that
Subtract equation (1) from equation (2) we get,
Substitute value of b in equation (1) we get
Hence, length and width of the rectangle 25 m and 17 m respectively
4) The perimeter of a rectangle is 42 cm. One side is 9 cm longer than the other side. Find the lengths of the
sides.
A) width 18, length 23 B) width 20, length 20 C) width 6, length 15 D)
width 23, length 18
Solution: Suppose that the one side of the rectangle be x cm, then the other side will be cm. Since
perimeter is 42 cm, this implies that
Hence, one side is 6 cm and other side is 15 cm. therefore, option (C) is correct.
5) Ellen wishes to mix candy worth $1.80 per pound with candy worth $2.40 per pound to form 48 pounds of a
mixture worth $2.00 per pound. How many pounds of the more expensive candy should she use?
Solution: Suppose x number of candies worth $ 1.80 per pound, then will be the number of candies
worth$2.40 per pound. According to the question

MAT 1100 Quantitative Reasoning Module 3 Lesson 3 Assignment 2
Simplify we get,
Hence, more expensive candy should be
6) An orchard operator must dilute 11 quarts of a 60% insecticide solution by adding water. How many quarts
of water should be added to get a mixture that is 2% insecticide?
A) 319 quarts B) 19 quarts C) 119 quarts D) 219 quarts
Solution: Suppose that x number of quarts of water has to be added to get a mixture that is 2% insecticide. Then
according to the question
11 quarts of 60% insecticide + x quarts of 0% insecticide = quarts of 2% insecticide
Simplify we get,
Hence, option (A) is correct.
7) Mardi received an inheritance of $50,000. She invested part at 7% and deposited the remainder in tax-free
bonds at 11%. Her total annual income from the investments was $4300. Find the amount invested at 7%.
Solution: Suppose that x be the amount invested at 7%, and then will be the amount invested at
11%. According to the question
Simplify we get,

MAT 1100 Quantitative Reasoning Module 3 Lesson 3 Assignment 2
Hence, the amount invested at 7% was
8) Roberto invested some money at 6%, and then invested $2000 more than twice this amount at 12%. His total
annual income from the two investments was $4440. How much was invested at 12%?
A) $28,000 B) $3000 C) $6000 D) $30,000
Solution: Suppose that he was invested $ x at 6%, this implies that he invested at 12%. Then
according to the question
Simplify we get,
Hence, he invested at 12%. Therefore option (D) is correct.
9) The speed of a stream is 5 mph. If a boat travels 74 miles downstream in the same time that it takes to travel
37 miles upstream, what is the speed of the boat in still water?
Solution: Suppose that the speed of the boat in still water is x mph. Then
Speed downstream
Speed upstream
Since, boat travels 74 miles downstream in the same time that it takes to travel 37 miles upstream, this implies
that

MAT 1100 Quantitative Reasoning Module 3 Lesson 3 Assignment 2
Hence, the speed of boat in still water is 15 mph.
10) An airplane travels 800 miles against the wind in 4 hours, and makes the return trip with the same wind in 2
hour(s). Find the rate of the wind.
A) 400 mph B) 100 mph C) 200 mph D) 300 mph
Solution: Suppose that the x be the rate of plane in still air and y be the wind speed. This implies that be
the rate of airplane with wind and be the rate of airplane against wind. According to the question
And
Subtract equation (1) from equation (2) we get,
Hence, rate of wind is 100 mph. therefore, option (B) is correct.