The bar chart shows the number of goals scored by a football team in each of five seasons. (a) Calculate the percentage increase in the number of goals from...

The bar chart gives \(42\) goals in season \(1\) and \(60\) goals in season \(5\). Percentage change is always measured against the original value, which here is the season \(1\) figure.

(a) Using \(\text{percentage increase}=\frac{\text{increase}}{\text{original}}\times 100\):

\[ \frac{60-42}{42}\times 100 \] [M1]

\[ =\frac{18}{42}\times 100=42.857\ldots \]

Correct to \(1\) decimal place the increase is \(42.9\%\). [A1]

Dividing by \(60\) instead of \(42\) gives \(30\%\) and is the standard error here. The question asks how much the goals grew relative to where they started, so \(42\) is the denominator.

(b) Scoring \(15\%\) fewer than season \(5\) means keeping \(100\%-15\%=85\%\) of \(60\), so the multiplier is \(0.85\).

\[ 60\times 0.85 \] [M1]

\[ =51 \]

The team scores \(51\) goals in season \(6\). [A1]

Working out \(15\%\) of \(60=9\) and subtracting to get \(60-9=51\) is equally acceptable. The single multiplier is quicker and is essential once repeated changes appear.