Finding the Unknown | FIO

Question 23

The height of a giraffe is two and a half metres more than half its height. How tall is the giraffe?

Solution

We will write an equation to represent the giraffe's height and then solve it.

Step 1 — Setting up the equation

First, we need to represent the giraffe's height. Let us call the giraffe's height 'x' metres. The problem gives us information about its height. It says the height 'x' is equal to something. This "something" is 'two and a half metres more than half its height'. Half of its height is $x/2$ . Two and a half metres is $2 \frac{1}{2}$ . So, we can write this as an equation.

$x = \frac{x}{2} + 2 \frac{1}{2}$

We can write $2 \frac{1}{2}$ as a fraction. This is the same as $2 + \frac{1}{2}$ . We can write 2 as $\frac{4}{2}$ . So, $2 \frac{1}{2}$ becomes $\frac{4}{2} + \frac{1}{2}$ . This adds up to $\frac{5}{2}$ .

$x = \frac{x}{2} + \frac{5}{2}$

$\boxed{x = \frac{x}{2} + \frac{5}{2}}$

Diagram 1

Step 2 — Solving for x

Now, we need to find the value of 'x'. We want to gather all the 'x' terms on one side. We can subtract $x/2$ from both sides of the equation. This moves the $x/2$ term to the left side.

$x - \frac{x}{2} = \frac{5}{2}$

On the left side, we have $x$ minus $x/2$ . This is like having one whole 'x' and taking away half of 'x'. So, we are left with half of 'x'.

$\frac{x}{2} = \frac{5}{2}$

Now, we have $x/2$ on the left side. We have $5/2$ on the right side. To find 'x', we can multiply both sides by 2. This will remove the division by 2 from 'x'.

$x = \frac{5}{2} \times 2$

When we multiply $\frac{5}{2}$ by 2, the '2' in the numerator and denominator cancel out. So, we are left with 5.

$x = 5$

This means the height of the giraffe is 5 metres.

$\boxed{x = 5 \text{ m}}$

Answer

The height of the giraffe is 5 m.

More questions in FIO

Solve these equations and check the solutions.

(a) $3x - 10 = 35$ (b) $5s = 3s$ (c) $3u - 7 = 2u + 3$ (d) $4(m + 6) - 8 = 2m - 4$ (e) $\frac{u}{15} = 6$

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[Hint: 4 more than a number, and 5 more than a number can never be equal!]

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Find the value of each unknown:

(a) $2y = 60$ (b) $-8 = 5x - 3$ (c) $-53w = -15$ (d) $13 - z = 8$ (e) $k + 8 = 12 - k$ (f) $7m = m - 3$ (g) $3n = 10 + n$

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Fill in the blanks with integers.

(a) $5 \times \underline{\quad} - 8 = 37$

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Q10

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Q11

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Q12

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Q13

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Q14

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Q15

The sum of two numbers is 76. One number is three times the other number. What are the numbers?

Q16

The figure shows the diagram for a window with a grill. What is the gap between two rods in the grill?

Q17

In a restaurant, a fruit juice costs ₹15 less than a chocolate milkshake. If 4 fruit juices and 7 chocolate milkshakes cost ₹600, find the cost of the fruit juice and milkshake.

Q18

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Q19

The steps to solve three equations are shown below. Identify and correct any mistakes.

(a) $6x + 9 = 66$

$x + 9 = 11$

$x = 11 - 9$

$x = 2$

(b) $14y + 24 = 36$

$7y + 12 = 18$

$7y = 6$

$y = \frac{6}{7}$

$4x = 9x + 8 - 5$

$4x = 9x + 3$

$4x - 9x = 3$

$-5x = 3$

$x = \frac{-5}{3}$

Q20

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Q21

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Q22

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Q23

The height of a giraffe is two and a half metres more than half its height. How tall is the giraffe?

Q24

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(a) How many squares are in position number 11 of the sequence? (b) How many sticks are needed to make the arrangement in position number 11 of the sequence? (c) Can an arrangement in this sequence be made using exactly 85 sticks? If yes, which position number will it correspond to? (d) Can an arrangement in this sequence be made using exactly 150 sticks? If yes, which position number will it correspond to?

Q25

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Q26

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(e) $6(x - 1) = 2(x - 1) - 4$

(f) $3 - 7s = 7 - 3s$

(g) $2x + 1 = 6 - (2x - 3)$

(h) $10 - 5x = 3(x - 4) - 2(x - 7)$

Q27

Solve the equations to find a path from Start to the End. Show your work in the given boxes provided and colour your path as you proceed.