Ratio and Proportion: Question 1

Worked solution

Part (a)

The ingredients flour, butter and sugar are shared in the ratio $5 : 3 : 2$.

Step 1: Find the total number of parts.

$5 + 3 + 2 = 10 \text{ parts}$

Step 2: Find the value of one part.

The total mass is $800\text{ g}$, and this is shared into $10$ equal parts:

$1 \text{ part} = \frac{800}{10} = 80\text{ g}$

Step 3: Find the mass of butter.

Butter corresponds to $3$ parts:

$\text{butter} = 3 \times 80 = 240\text{ g}$

$\boxed{\text{Butter} = 240\text{ g}}$

Check: flour $= 5 \times 80 = 400\text{ g}$, butter $= 240\text{ g}$, sugar $= 2 \times 80 = 160\text{ g}$, and $400 + 240 + 160 = 800\text{ g}$. ✓

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Part (b)

Now the baker uses $450\text{ g}$ of flour. Flour corresponds to $5$ parts.

Step 1: Find the value of one part using the flour amount.

$5 \text{ parts} = 450\text{ g} \quad\Rightarrow\quad 1 \text{ part} = \frac{450}{5} = 90\text{ g}$

Step 2: Find the total mass.

The total is $10$ parts:

$\text{total} = 10 \times 90 = 900\text{ g}$

$\boxed{\text{Total mass} = 900\text{ g}}$

Alternative method (using fractions/proportion).

Flour is $\dfrac{5}{10} = \dfrac{1}{2}$ of the whole mixture. So the flour mass is half of the total:

$\text{total} = 450 \times \frac{10}{5} = 450 \times 2 = 900\text{ g}$

Both methods give the same result.

Check: with $1$ part $= 90\text{ g}$, butter $= 3 \times 90 = 270\text{ g}$ and sugar $= 2 \times 90 = 180\text{ g}$; then $450 + 270 + 180 = 900\text{ g}$. ✓