Name: ___________________________________
Date: _______________________________
3.5 Modelling With Algebra (part 2)
Minds on:
1. Lake Ontario is 77km shorter than Lake Erie. The lengths of the two lakes total 699km. Write
an equation to find the length of Lake Ontario.
2. Fred has $10 more than Barney. Together, they have $120. Write an equation to find the
amount they have.
3. The area of the triangle is three times the area of a square. The sum of their areas is 230m³.
Write an expression to represent their areas.
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MPM1DY
Mr. V
VSS
Grade 9 Academic Math
Lesson learning goals:
•
•
Model a problem using algebra
Solve algebraic models using a variety of methods
When modelling with algebra, ensure the follow these steps for full marks:
1.
2.
3.
4.
5.
write the introductory sentence(s) identifying the variables
write the equation
simplify the equation
solve (if needed)
write a concluding sentence
1. The sum of three consecutive odd integers is 57.
a) Let x represent the least integer. Write an algebraic expression to represent each of the other
integers.
b) Write an equation to represent the sum of the integers.
c) Find the integers.
2. Three consecutive even integers have a sum of 102.
a) Write an algebraic expression to represent each integer.
b) Write an equation to represent the sum of the integers.
c) Find the integers.
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MPM1DY
Mr. V
VSS
Grade 9 Academic Math
3. The length of a rectangle is triple its width. The perimeter of the rectangle is 40 cm. What are the
length and width?
4. The sum of two numbers is 42. One number is 8 less than the other. What are the two numbers?
5.The sides of a triangle are 3 consecutive whole numbers in centimetres. The perimeter of the
triangle is 48cm. How long is each side?
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MPM1DY
Mr. V
VSS
Grade 9 Academic Math
6. A large painting costs $75 more than a smaller painting. Together, they cost $725. How much does
each cost?
7. A parking meter contains $27.05 in quarters and dimes. There are 146 coins. How many quarters
are there?
8. Determine expressions to represent the dimensions of a rectangular prism V = x3 + 5x2 + 6x when
x = 3cm.
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