 New Zealand
Level 7 - NCEA Level 2

Equation Problem Solving with 2 Variables

Interactive practice questions

The sum of two integers is $70$70.

a

If one of the integers is $29$29, what is the other integer?

b

Let one of the integers be $x$x. Write an expression for the other integer.

c

Hence write an expression for the product $y$y of the two integers. Give your answer in expanded form.

d

When $x=35$x=35, what is the product of the two integers?

e

When $x=35$x=35, does this result in the largest possible product?

Yes

A

No

B

Yes

A

No

B
Easy
Approx 3 minutes

A rectangular enclosure is to be built for an animal. Zookeepers have $26$26 metres of fencing, but they want to maximise the area of the enclosure.

Let $x$x be the width of the enclosure.

A cube has side length $7$7 cm and a mass of $1715$1715 g. The mass of the cube is directly proportional to the cube of its side length.

A rectangle is such that its length is $2$2 times its width.

Let $A$A represent the area of the rectangle and $w$w represent its width.

Outcomes

M7-7

Form and use linear, quadratic, and simple trigonometric equations

91257

Apply graphical methods in solving problems

91261

Apply algebraic methods in solving problems