Nunuboy1994 wrote:

Gnpth wrote:

The price of a radio was increased by 25 percent. The new price was then increased by 40 percent. A single increase of what percent is equivalent to these two successive increases?

A. 80%

B. 75%

C. 65%

D. 50%

E. 45%

We can apply a few simple formulas to sovle this

x(1.25)

x(1.40)

let x be 10 so really just

1.25x1.40 = 1.75

Thus

"B"

I might be mistaken, but I think you mean let x be 1.

For successive percent changes, if the question asks for overall percent change (and not, e.g., for the new or old price), you can just multiply the multipliers, and if the result is bigger than 1,then subtract 1 . . .

IF x = 1 (which it can and does in the product of multipliers method).

As you noted, a 25% increase = 1 + .25 = 1.25

Another 40% increase is 1.40

Multiply the multipliers: (1.25)*(1.4) = 1.75

Overall or "single" percent change is

(1.75 - 1) *100 = .75 *100 = 75%

If x = 10, it looks, from the way it's written, as if you'd subtract 10 from 1.75, leaving -8.25.

Maybe you meant:

10 * 1.75 = 17.5

17.5 - 10 = 7.5

\(\frac{7.5}{10}\) = .75*100 = 75%

Bottom line is just that if you use 1 as original value, you can simply multiply the multipliers, and if result is greater than 1, then subtract 1 to get percent change / increase in decimal form.

If you use 10, you can multiply that by the product of the multipliers (1.75), and then do

\(\frac{change}{original}\), to get percent change / increase.

You can't, however, just subtract 10 from the multipliers' product in the same way that, using x = 1, you can just subtract 1.