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The Smith family has an annual income of Gh¢15,000.00. They planned to budget it in the following way: Make a pie chart to show the distribution of the money. What fraction of the money is spent on savings?

Mathematics

ScanSolve AI Answer

Step 1: Calculate the central angle for each expense category for the pie chart.
The total percentage is 100%, which corresponds to a full circle of 360∘360^\circ.

  • Food: 10100×360∘=36∘\frac{10}{100} \times 360^\circ = 36^\circ
  • Shelter: 25100×360∘=90∘\frac{25}{100} \times 360^\circ = 90^\circ
  • Clothing: 20100×360∘=72∘\frac{20}{100} \times 360^\circ = 72^\circ
  • Advancement: 15100×360∘=54∘\frac{15}{100} \times 360^\circ = 54^\circ
  • Operating expenses: 18100×360∘=64.8∘\frac{18}{100} \times 360^\circ = 64.8^\circ
  • Savings: 12100×360∘=43.2∘\frac{12}{100} \times 360^\circ = 43.2^\circ

1.i) Make a pie chart to show the distribution of the money.
To draw the pie chart, divide a circle into sectors with the following central angles:

  • Food: 36∘36^\circ
  • Shelter: 90∘90^\circ
  • Clothing: 72∘72^\circ
  • Advancement: 54∘54^\circ
  • Operating expenses: 64.8∘64.8^\circ
  • Savings: 43.2∘43.2^\circ

1.ii) What fraction of the money is spent on savings?
From the table, the percentage spent on savings is 12%.
To express this as a fraction, we write 12% as 12100\frac{12}{100}.

Fraction for savings=12100\text{Fraction for savings} = \frac{12}{100}

Simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 4.

12÷4100÷4=325\frac{12 \div 4}{100 \div 4} = \frac{3}{25}

The fraction of the money spent on savings is 325\boxed{\frac{3}{25}}.

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