Download Systems of Equations – Application Problems

Systems of Equations – Application Problems
Math 10 Academic
1. Candice needs to have two small rooms in her house painted. She is going to hire a painter.
The first painter said that he would charge a flat fee of $150 to cover materials and travel,
plus $30 per hour. The second painter said that she would charge a flat fee of $165, plus
$25 per hour.
(a) Determine the equation of the linear function that describes the cost, c, of using the first
painter in terms of the number of hours, h, he works.
(b) Determine the equation of the linear function that describes the cost, c, of using the
second painter in terms of the number of hours, h, she works.
(c) Determine at how many hours will the cost be the same.
2. Porter Pools charges $30 for a service call, plus $45 per hour for labour. Bailey Pools and
Spas charges $50 for a service call, plus $40 per hour for labour. Find the length of a
service call for which both companies charge the same amount.
3. The difference of two numbers is 5. Twice the larger number plus three times the smaller
number is 45. Find the numbers.
4. Ajay is draining two different tanks using two different pumps. The first tank holds 85
litres and is being drained by a pump that removes 7 litres per minute. The second tank
holds 64 litres and is being drained by a pump that removes 4 litres per minute. Assuming
that the tanks were initially fully and that the pumps were turned on at the same time, at
what time will the tanks have the same number of litres of fluid?
5. Nita is going to organize a 50th wedding anniversary party for her parents. She wants to
rent a banquet hall and have a buffet. The local legion hall charges a flat rate of $185 for
the hall, plus $10 per person for the buffet. The voluntary fire department and its
auxiliary charge a flat rate of $215 for their hall and $8.50 per person for the buffet.
Determine the number of people who would have to attend in order for the two
organizations to charge the same amount.
6. The sum of two numbers is 12. If you double the first number and triple the second
number, then the new sum is 27. Find the numbers.
7. The perimeter of a rectangular garden is 174 metres. The length of the garden is twelve
more than twice the width. Find the length and width.
8. If Jacob buys 4 hamburgers and 1 container of french fries, he pays $15. If he purchases 6
hamburgers and 3 containers of french fries, he pays $24. How much does hamburger
cost? How much does a container of french fries cost?