Given that 𝑋 = 𝑎𝑏, find the percentage increase in X when both a and b increase by 12%.

Question

mathhelper · Accepted Answer

new a value is 1.2a new b value is 1.2b new X value = (1.2a)(1.2b) = 1.44ab increase is 44% e.g. suppose a = 60 and b = 80 old X = 4800 new a = 1.2(60) = 72 new b = 1.2(80) = 96 new X = (72)(96) = 6912 6912/4800 = 1.44 or 144% so it increased by 44%

connie · Answer

Thank you

Step-by-Step Bot · Answer

To find the percentage increase in X when both a and b increase by 12%, we can follow these steps: Step 1: Calculate the new values of a and b after a 12% increase. - Let's assume the original values of a and b are: - a = A - b = B - After a 12% increase, the new values of a and b will be: - New a = A + 0.12A = 1.12A - New b = B + 0.12B = 1.12B Step 2: Calculate the new value of X using the new values of a and b. - Given that X = ab, the new value of X will be: - New X = (1.12A)(1.12B) = (1.12)^2 * (AB) Step 3: Calculate the percentage increase in X. - The percentage increase in X can be calculated using the formula: - Percentage Increase = (New X - Old X) / Old X * 100 - Old X = AB (original value of X) - New X = (1.12)^2 * (AB) - Percentage Increase = [(1.12)^2 * (AB) - AB] / AB * 100 Simplifying this equation will give us the percentage increase in X when both a and b increase by 12%.

Explain Bot · Answer

To find the percentage increase in X when both a and b increase by 12%, we can follow these steps: 1. Start with the given equation: 𝑋 = 𝑎𝑏. 2. Let's assume initial values for a and b and calculate the initial value of X. For example, assume a = 100 and b = 200. In this case, X = 100 * 200 = 20,000. 3. Now, let's calculate the new values of a and b after increasing them by 12%. - Increased value of a = (initial value of a) + (12% of initial value of a) = 100 + (0.12 * 100) = 112. - Increased value of b = (initial value of b) + (12% of initial value of b) = 200 + (0.12 * 200) = 224. 4. Substitute the increased values of a and b back into the equation 𝑋 = 𝑎𝑏. - New value of X = 112 * 224 = 25,088. 5. Calculate the percentage increase in X using the formula: - Percentage Increase = [(New Value - Initial Value) / Initial Value] * 100. - Percentage Increase = [(25,088 - 20,000) / 20,000] * 100 = 25.44%. Therefore, the percentage increase in X when both a and b increase by 12% is approximately 25.44%.