Writing Formulae Worksheet worksheet - Free Printable

Problem: Writing Formulae Worksheet

We will solve each part of the worksheet step by step.

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#### Question 1: Florist Bouquets
A florist always prepares 3 more bouquets than the number of orders she receives.

##### Part (a): Write a calculation to work out how many bouquets the florist will make.

- i. 5 orders
- Calculation: Number of bouquets = Number of orders + 3
- Substituting 5 for the number of orders:
\[
\text{Number of bouquets} = 5 + 3 = 8
\]

- ii. 8 orders
- Calculation: Number of bouquets = Number of orders + 3
- Substituting 8 for the number of orders:
\[
\text{Number of bouquets} = 8 + 3 = 11
\]

##### Part (b): Complete this function machine in words, then letters.

- Words: Add 3 to the number of orders.
- Letters:
\[
\text{number of orders} \rightarrow +3 \rightarrow \text{number of bouquets made}
\]

##### Part (c): Complete this formula in words for the number of bouquets the florist makes.

- Formula in words: The number of bouquets made is equal to the number of orders plus 3.
- Formula:
\[
\text{number of bouquets made} = \text{number of orders} + 3
\]

##### Part (d): Complete the formula in letters for the number of bouquets the florist makes.

- Let \( n \) represent the number of orders and \( b \) represent the number of bouquets.
- Formula:
\[
b = n + 3
\]

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#### Question 2: Cupcakes and Butter
To make cupcakes, you need 10 grams of butter per cupcake.

##### Part (a): Complete the function machine.

- Function machine:
\[
\text{number of cupcakes} \rightarrow \times 10 \rightarrow \text{total amount of butter}
\]

##### Part (b): Write a formula to work out the amount of butter, \( b \), you use when you know the number of cupcakes, \( c \).

- Formula:
\[
b = 10 \times c
\]

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#### Question 3: Muffins and Caster Sugar
To make muffins, you need 12 grams of caster sugar per muffin.

##### Part (a): Write a formula to work out the amount of caster sugar, \( s \), for the number of muffins, \( m \).

- Formula:
\[
s = 12 \times m
\]

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#### Question 4: Medication for Children
To work out the amount of medication in millilitres that a child needs, you divide the mass of the child, in kilograms, by 10.

##### Part (a): Write a formula that connects the amount of medication, \( a \), to the mass of a child, \( m \).

- Formula:
\[
a = \frac{m}{10}
\]

##### Part (b): Use your formula to work out the amount of medication needed for a child with a mass of:

- i. 30 kg
- Substituting \( m = 30 \) into the formula:
\[
a = \frac{30}{10} = 3 \text{ mL}
\]

- ii. 46 kg
- Substituting \( m = 46 \) into the formula:
\[
a = \frac{46}{10} = 4.6 \text{ mL}
\]

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Final Answers:

1.
- (a) i. 8 bouquets, ii. 11 bouquets
- (b) Words: Add 3 to the number of orders; Letters: \( \text{number of orders} \rightarrow +3 \rightarrow \text{number of bouquets made} \)
- (c) Formula: \( \text{number of bouquets made} = \text{number of orders} + 3 \)
- (d) Formula: \( b = n + 3 \)

2.
- (a) Function machine: \( \text{number of cupcakes} \rightarrow \times 10 \rightarrow \text{total amount of butter} \)
- (b) Formula: \( b = 10 \times c \)

3.
- Formula: \( s = 12 \times m \)

4.
- (a) Formula: \( a = \frac{m}{10} \)
- (b) i. 3 mL, ii. 4.6 mL

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Boxed Final Answer:

\[
\boxed{
\begin{array}{l}
\text{1. (a) i. 8, ii. 11} \\
\text{ (b) Words: Add 3 to the number of orders; Letters: } \text{number of orders} \rightarrow +3 \rightarrow \text{number of bouquets made} \\
\text{ (c) } \text{number of bouquets made} = \text{number of orders} + 3 \\
\text{ (d) } b = n + 3 \\
\text{2. (a) } \text{number of cupcakes} \rightarrow \times 10 \rightarrow \text{total amount of butter} \\
\text{ (b) } b = 10 \times c \\
\text{3. } s = 12 \times m \\
\text{4. (a) } a = \frac{m}{10} \\
\text{ (b) i. 3 mL, ii. 4.6 mL}
\end{array}
}
\]