Question

6 the perimeter of a rectangle is 36 cm. if the length of the rectangle is twice its width, determine its dimensions.
7 the sum of two numbers \\(x\\) and \\(y\\) is 52. the difference between the two numbers is 8. find the values of \\(x\\) and \\(y\\).
8 the sum of two numbers is 35 and their difference is 19. find the numbers.
9 bruce is 4 years older than michelle. if their combined age is 70, determine their individual ages.
10 a boy is 6 years older than his sister. in three years time he will be twice her age. what are their present ages?

Explanation:

Solve Question 6

Using the Linear Equations and Systems of Linear Equations knowledge points
Let \(w\) be the width and \(l\) be the length.

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Solve Question 7

Using the Systems of Linear Equations and Elimination Method knowledge points

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Solve Question 8

Using the Systems of Linear Equations and Elimination Method knowledge points
Let the two numbers be \(a\) and \(b\) with \(a > b\).

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Solve Question 9

Using the Systems of Linear Equations and Substitution Method knowledge points
Let \(B\) be Bruce's age and \(M\) be Michelle's age.

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Solve Question 10

Using the Systems of Linear Equations and Substitution Method knowledge points
Let \(b\) be the boy's present age and \(s\) be the sister's present age.

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Answer:

Question 6

The dimensions of the rectangle are:
Length = \(12\text{ cm}\), Width = \(6\text{ cm}\)

Question 7

\(x = 30\), \(y = 22\)

Question 8

The numbers are \(27\) and \(8\).

Question 9

Bruce's age is \(37\) years old, and Michelle's age is \(33\) years old.

Question 10

The boy's present age is \(9\) years, and the sister's present age is \(3\) years.