Download Solving Problems

Solving Problems – Part I
(using LINEAR SYSTEMS)
I. NUMBER PROBLEMS
Barney reads for twice as many hours per week as Fred. Together
they read for a total of 36 hours in one week. Determine the number
of hours that each person spends reading that week.
Step #1: Define the variables.
Let 𝑥 represent _____________________ and 𝑦 represent _____________________.
Step #2: Write a system of equations relating the given variables.


Step #3: Solve the system of equations using substitution or elimination.
Step #4: Write a conclusion to the given problem.
 _________________________________________________________
Step #5: Check, using the facts given in the problem.
II. MONEY PROBLEMS
Joey works at a theatre selling popcorn. Large boxes sell
for $5 and small boxes sell for $3. During his shift, he sold
80 boxes of popcorn for a total of $306. Determine how
many boxes of popcorn of each size that Joey sold.
HOMEWORK
1.
Textbook exercises:
2.
Additional problems:
p.46 – 47 #1 – 3, 11, 12, 15
1. In hockey, the number of points a player scores is equal to the sum of their goals
and assists. In the 1998–99 NHL season, Mats Sundin scored 83 points. He scored
21 fewer goals than assists. Determine the number of goals and assists earned by
Sundin.
2. A golf club charges members an annual fee and a greens fee for each round of golf
played. One year, one member played twelve rounds of golf and paid $814.
Another member played twenty-nine rounds and paid $1188. Determine the annual
fee and the greens fee.
3. Twice Sari’s age plus half her mother’s age is 48. Three times Sari’s age less half
her mother’s age is 27. Determine Sari and her mother’s ages.
4. When three numbers are added in pairs, the sums of the pairs are 22, 39, and 45.
Determine the three numbers.
Answers
1. 31 goals, 52 assists
3. 15 years, 36 years
2. $550 annual fee, $22 greens fee
4. 8, 14, 31
HOMEWORK QUESTIONS
1.
When 6 times the larger of two numbers is added to 7 times the smaller, the
result is 114. Ten times the larger less 9 times the smaller is 66. Determine the
numbers.
2.
The pop machine contained $3.05 made up of dimes and quarters. There were
20 coins in all. Determine the number of dimes.
3.
The sum of Barney’s age and his father’s age is 67. Three times Barney’s age
increased by 7 is his father’s age. Determine Barney’s age.
4.
Seven times the smaller of two numbers plus 9 times the larger is 178. When 10
times the larger is increased by 11 times the smaller, the result is 230.
Determine the numbers.
5.
The sum of two numbers is 1990. When 318 is subtracted from five times the
smaller the result is three times the smaller. Determine the numbers.
6.
Ivan has 34 bills in fives and twos. The total value of these bills is $116. 00.
Determine the number of $2 bills.
7.
The automatic sandwich machine contained 132 coins in dimes and quarters.
The value of the coins was $21.30. Determine the number of quarters.
8.
One-half of Wilma’s age plus one-third of Betty’s age is 24. One-fifth Wilma’s
age less one-ninth of Betty’s age is 3. Determine Betty’s age.
9.
Fred is 3 times older than his dog, Dino. Four years ago, he was 7 times older.
Determine Dino’s age.
10.
Complete question #20 on page 45 of the textbook.
ANSWERS
1.
3.
5.
7.
9.
6 and 12
15 years old
159 and 1831
54 quarters
6 years old
2.
4.
6.
8.
10.
13 dimes
10 and 12
18 bills
27 years old
8, 14, and 31