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Two numbers are, respectively, 17% and 5...

Two numbers are, respectively, 17% and 50% more than a third number. The ratio of the two numers is

A

`39:50`

B

`50:39`

C

`59:39`

D

`39:59`

Text Solution

AI Generated Solution

The correct Answer is:
To find the ratio of the two numbers that are respectively 17% and 50% more than a third number, we can follow these steps: ### Step 1: Define the third number Let the third number be \( x \). ### Step 2: Calculate the first number The first number is 17% more than the third number. Therefore, we can express the first number as: \[ \text{First Number} = x + 0.17x = 1.17x \] ### Step 3: Calculate the second number The second number is 50% more than the third number. Thus, we can express the second number as: \[ \text{Second Number} = x + 0.50x = 1.50x \] ### Step 4: Write the ratio of the two numbers Now, we can write the ratio of the first number to the second number: \[ \text{Ratio} = \frac{\text{First Number}}{\text{Second Number}} = \frac{1.17x}{1.50x} \] ### Step 5: Simplify the ratio The \( x \) in the numerator and denominator cancels out: \[ \text{Ratio} = \frac{1.17}{1.50} \] To simplify this fraction, we can multiply both the numerator and the denominator by 100 to eliminate the decimals: \[ \text{Ratio} = \frac{117}{150} \] ### Step 6: Further simplify the ratio Now, we can simplify \( \frac{117}{150} \) by finding the greatest common divisor (GCD) of 117 and 150. The GCD is 3: \[ \frac{117 \div 3}{150 \div 3} = \frac{39}{50} \] ### Final Answer Thus, the ratio of the two numbers is: \[ \text{Ratio} = 39 : 50 \] ---
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