MPM 2D1
Name:
Date:
Linear Systems – Practice
1.
The sum of 2 numbers is 778 and their difference is 282. Find the numbers
2.
The sum of 2 numbers is 812 and their difference is 42. Find the numbers.
3.
Three times the smaller number increased by five times the larger number is 229. Four times the
smaller decreased by 25 equals 3 times the larger. Find the numbers.
4.
The bookstore at the school has 130 math and history books. A math book costs $19.00 and a
history book costs $16.20. If the total bill was $2274.00, how many math books were bought at the
store?
5.
A parking meter contained $8.60 made up of dimes and nickels. If there are 110 coins, how many
dimes are there in the parking meter?
6.
The length of a rectangle is 19 m longer than the width. If the perimeter is 606 m, what are the
dimensions of the rectangle?
7.
The perimeter of a rectangle is 176 m. The length is equal to 3 times the width, decreased by 4.
Find the dimensions of the rectangle.
8.
Adult and student tickets were sold for the school play. The total receipts were $2005. The number
of student tickets sold was equal to three times the number of adult tickets sold decreased by 56. If
student tickets cost $3.50 and adult tickets cost $5.00, how many adult tickets were sold?
9.
Wayne invested $9000, part at 9%/annum and the remainder at 8%/annum. After one year the total
interest from these investments was $750. How much was invested at 9%?
10.
The student council invested $4000, part at 8.5% interest per annum and the remainder at 9.5% per
annum. After one year, the interest from the investment at 8.5% was $16 more than the interest
from the investment at 9.5%. How much was invested at 9.5%?
11.
It took Callum 7 hours to drive the 390 km from Cold Bay to Morgan’s Cove. He averaged
60 km/h for the first part of the trip, but was forced to complete the trip at 50 km/h due to a
thunderstorm. How many hours did he spend driving at 50 km/h?
12.
Holly took a trip of 1900 km, travelling by bus and plane. The bus averaged 60 km/h and the plane
700 km/h. If the total trip took 5 hours, how many kilometres did she travel by bus?
MPM 2D1
Name:
Date:
Answers:
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Let x be the first number
Let y be the second number
Let x be the first number
Let y be the second number
Let x be the smaller number
Let y be the bigger number
Let x be the number of math books
Let y be the number of history books
Let x be the number of 10¢ coins
Let y be the number of 5¢ coins
Let x be the length
Let y be the width
Let x be the length
Let y be the width
Let x be number of adult tickets
Let y be the number of children’s tickets
Let x be amount invested at 9%
Let y be amount invested at 8%
Let x be amount invested at 8,5%
Let y be amount invested at 9,5%
Let x be the time at 60 km/h
Let y be the time at 50 km/h
Let x be the distance at 60 km/h
Let y be the distance at 700 km/h
x + y = 778
x – y = 282
x + y = 812
x – y = 42
3x + 5y = 229
4x – 25 = 3y
x + y = 130
19x + 16.20y = 2274
x + y = 110
10x + 5y = 860
x = y + 19
2x + 2y = 606
2x + 2y = 176
x = 3y – 4
5x + 3.50y = 2005
y = 3x – 56
x + y = 9000
0.09x + 0.08y = 750
x + y = 4000
0.085x = 0.095y + 16
60x + 50y = 390
x+y=7
x + y = 1900
x
y
+
=5
60 700
Number (x) = 530
Number (y) = 248
Number (x) = 427
Number (y) = 385
Smaller = 28
Bigger = 29
Math books = 60
10¢ coins = 62
Length = 161 m
Width = 142 m
Length = 65 m
Width = 23 m
Adult tickets = 142
Invested at 9% = $3000
Invested at 9,5% = $1800
Time during
thunderstorm = 3 h
On bus = 150 km