Mathematics (Syllabus D) 4024/21 — May/June 2019

Walkthrough

Lauren's monthly income is 1800. Her total spending is the sum of the five items given: $500 + 250 + 120 + 240 + 70 = 1180$. Because she saves the rest, her savings is $1800 - 1180 = 620$. To find what percentage of 1800 this is, divide 620 by 1800 and multiply by 100:

$\frac{620}{1800} \times 100 = 34.44\ldots$

So she saves $34.4\%$ of her monthly income.

Key Takeaways

A percentage is a part divided by the whole, then multiplied by 100. Here the whole is the monthly income, not the total spending. The part is the saved money, 620.

Common Mistakes

One common mistake is forgetting one of the five expenses, especially Travel or Clothes. Another is calculating the percentage spent rather than the percentage saved; if you do that, you must subtract from 100. A third mistake is omitting the $\times 100$ step, which leaves the answer as a ratio instead of a percentage.

Things to Be Careful About

The key figure 620 must be shown as $1800 - 1180$. The fraction must be $620/1800$, not $1180/620$. On a Calculator paper you may evaluate 34.44... on the calculator; showing the fraction in the working guards the method mark. The mark scheme allows 34.4 or 34.44 to 34.45, so 34.4% is accepted.

Walkthrough

The current rent is 500. A rise of 3.6% means the new rent is 103.6% of the old rent. Converting 103.6% to a decimal multiplier gives 1.036, so the new rent is $500 \times 1.036 = 518$ dollars.

Alternatively, the increase itself is $500 \times 0.036 = 18$ dollars, so the new rent is $500 + 18 = 518$ dollars.

Key Takeaways

A percentage increase can be performed with one multiplication by the multiplier $1 + \text{(percentage as a decimal)}$. Here $1 + 0.036 = 1.036$.

Common Mistakes

The most common error is writing 1.36 instead of 1.036, which treats 3.6% as if it were 36%. Another is to find the amount of increase, $500 \times 0.036 = 18$, and then stop without adding it to the original 500.

Things to Be Careful About

The multiplier for a rise of 3.6% has three decimal digits: 1.036. The final rent is 518 dollars, which is a fall? Let me know: as if the original rent plus 18 dollars: 518. On the Calculator paper, direct multiplication is the fastest route, but showing $500 \times 1.036$ earns the method mark.