Question
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3. Write each increase as a percent. Illustrate each answer with a number line. a) The price of a house increased from \( \$ 210000 \) to \( \$ 225000 \). b) The elastic stretched from 10 cm to 13 cm .

Ask by Williams Tyler. in Canada
Feb 27,2025

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Answer

a) The house price increased by 7.14%. b) The elastic stretched by 30%. Illustrations: - For the house, the increase from $210,000 to $225,000 represents a 7.14% increase. - For the elastic, stretching from 10 cm to 13 cm is a 30% increase.

Solution

To write each increase as a percent, we need to calculate the percentage increase in the price of the house and the length of the elastic. a) Percentage increase in the price of the house: \[ \text{Percentage increase} = \left( \frac{\text{Increase in price}}{\text{Original price}} \right) \times 100 \] Given: Original price = $210,000 Increase in price = $225,000 - $210,000 = $15,000 \[ \text{Percentage increase} = \left( \frac{15000}{210000} \right) \times 100 = 7.14\% \] b) Percentage increase in the length of the elastic: \[ \text{Percentage increase} = \left( \frac{\text{Increase in length}}{\text{Original length}} \right) \times 100 \] Given: Original length = 10 cm Increase in length = 13 cm - 10 cm = 3 cm \[ \text{Percentage increase} = \left( \frac{3}{10} \right) \times 100 = 30\% \]

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To calculate the percentage increase for a house price from \( \$ 210,000 \) to \( \$ 225,000 \), we use the formula: \[ \text{Percentage Increase} = \left(\frac{\text{New Value} - \text{Old Value}}{\text{Old Value}}\right) \times 100 \] Here, it would be \[ = \left(\frac{225000 - 210000}{210000}\right) \times 100 = \left(\frac{15000}{210000}\right) \times 100 \approx 7.14\% \] On a number line, you can illustrate this by marking points for \( 210,000 \) and \( 225,000 \), indicating the increase. For the elastic's stretch from 10 cm to 13 cm, we apply the same percentage increase formula: \[ = \left(\frac{13 - 10}{10}\right) \times 100 = \left(\frac{3}{10}\right) \times 100 = 30\% \] On a number line, you can mark \( 10 \) cm and \( 13 \) cm with an arrow indicating the stretch.

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