shasadou wrote:

The number m is the average (arithmetic mean) of the positive numbers a and b. If m is 75% more than a, then m must be

A. 30% less than b

B. \(42 \frac{6}{7}\)% less than b

C. 50% less than b

D. \(66 \frac{2}{3}\)% less than b

E. 75% less than b

We can create the equation:

m = (a + b)/2

and

m = 1.75a

Substituting, we have:

1.75a = (a + b)/2

3.5a = a + b

2.5a = b

Using the percent change formula, we have:

(m - b)/b x 100

(1.75a - 2.5a)/(2.5a) x 100

Multiplying by 100/100, we have:

(175a - 250a)/250a x 100

-75a/250a x 100

-3/10 x 100 = 30% less

Alternate Solution:

We can let a = 100; then m = 175. We can create the equation:

(a + b)/2 = m

(100 + b)/2 = 175

100 + b = 350

b = 250

Using the percent change formula, we have:

(m - b)/b x 100 = (175 - 250)/250 x 100 = -30%, or 30% less.

Answer: A

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