Question

the number a is 180% greater than the number b. the number b is 45% less than 25. what is the value of a? a 20.25 b 24.75 c 33.75 d 38.50

Explanation:

Step1: Calculate the value of b

First, find the value of \( b \). Since \( b \) is 45% less than 25, we calculate \( b = 25\times(1 - 0.45) \).
\( 1 - 0.45 = 0.55 \), so \( b = 25\times0.55 = 13.75 \)? Wait, no, wait. Wait, 45% less than 25: the formula is \( \text{original} \times (1 - \text{percentage decrease}) \). So \( 25\times(1 - 0.45)=25\times0.55 = 13.75 \)? Wait, but then \( a \) is 180% greater than \( b \). Wait, 180% greater means \( a = b\times(1 + 1.8) \), because 100% is the original, so 180% greater is original plus 180% of original, so \( 1 + 1.8 = 2.8 \)? Wait, no, 180% greater than \( b \) means \( a = b + 1.8b = 2.8b \)? Wait, no, let's re - check.

Wait, percentage greater: if a number is \( x\% \) greater than another number, the formula is \( \text{number} = \text{original}\times(1+\frac{x}{100}) \). So 180% greater than \( b \) means \( a = b\times(1 + \frac{180}{100})=b\times(1 + 1.8)=b\times2.8 \). But first, let's recalculate \( b \).

Wait, 45% less than 25: \( 25 - 25\times0.45 = 25\times(1 - 0.45)=25\times0.55 = 13.75 \). Then \( a = 13.75\times(1 + 1.8)=13.75\times2.8 \). Wait, but 13.75×2.8: 13×2.8 = 36.4, 0.75×2.8 = 2.1, so 36.4+2.1 = 38.5? But that's option D. Wait, but maybe I made a mistake in calculating \( b \). Wait, wait, 45% less than 25: 25×0.45 = 11.25, 25 - 11.25 = 13.75. Then 180% greater than \( b \): 180% of \( b \) is \( 1.8b \), so \( a = b+1.8b = 2.8b \). 13.75×2.8: let's calculate 13.75×2 = 27.5, 13.75×0.8 = 11, so 27.5+11 = 38.5. So \( a = 38.5 \), which is option D.

Wait, but let's check again. Maybe the mistake is in the interpretation of "180% greater". Wait, "greater than" means the difference is 180% of \( b \), so \( a = b+1.8b = 2.8b \). And \( b = 25\times(1 - 0.45)=13.75 \). Then \( a = 13.75\times2.8 = 38.5 \), which is option D.

Step1: Calculate b

To find \( b \), which is 45% less than 25, we use the formula for percentage decrease:
\( b = 25\times(1 - 0.45) \)
\( 1 - 0.45 = 0.55 \), so \( b = 25\times0.55 = 13.75 \)

Step2: Calculate a

Since \( a \) is 180% greater than \( b \), we use the formula for percentage increase:
A number \( x\% \) greater than a number \( y \) is \( y\times(1+\frac{x}{100}) \).
For \( x = 180 \) and \( y = b = 13.75 \):
\( a = 13.75\times(1+\frac{180}{100})=13.75\times(1 + 1.8)=13.75\times2.8 \)
\( 13.75\times2.8=(13 + 0.75)\times2.8=13\times2.8+0.75\times2.8=36.4 + 2.1 = 38.5 \)

Answer:

D. 38.50