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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 Simmons Marshall. in Canada
Feb 27,2025

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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 find the percent increase for the house price, you subtract the original price from the new price: \( 225000 - 210000 = 15000 \). Then, divide that by the original price: \( 15000 / 210000 = 0.0714 \). Multiply by 100 to convert to a percentage, which gives you approximately a 7.14% increase. For the elastic, subtract the original length from the new length: \( 13 - 10 = 3 \). Divide this by the original length: \( 3 / 10 = 0.3 \). When multiplied by 100, it results in a 30% increase. On a number line, you can represent the house price by marking 210,000 and then moving to 225,000, demonstrating the increase. For the elastic, you’d mark 10 cm and then show the movement to 13 cm, visually illustrating the difference!

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