To find 125% of 1,400 using equivalent ratios, you can follow these steps:
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Understand the concept of percentage: The percentage 125% can be expressed as a fraction. Since 100% is equivalent to 1 (or 1 whole), 125% can be represented as \( \frac{125}{100} \).
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Simplify the fraction: \[ \frac{125}{100} = \frac{125 \div 25}{100 \div 25} = \frac{5}{4} \] So, 125% can also be expressed as the ratio \( 5:4 \).
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Set up the equivalent ratio: To find 125% of the 1,400 tickets, you can create an equivalent ratio comparing the unknown quantity (let's call it \( x \)) to the original total (1,400 tickets): \[ \frac{x}{1400} = \frac{5}{4} \]
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Cross-multiply to solve for \( x \): \[ 4x = 5 \times 1400 \] \[ 4x = 7000 \]
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Divide both sides by 4 to solve for \( x \): \[ x = \frac{7000}{4} = 1750 \]
So, 125% of 1,400 is \( x = 1,750 \).
Therefore, the Amazing Art Museum expects to sell 1,750 tickets, which is 125% of the 1,400 tickets they sold yesterday.