128 percent too high

when pilgrims counted noses, they got a count that was 128 percent too high. if they counted 9120 noses, what was the correct count? grade 9- middle school student asking

Hi,

If you had said "14% too high" then my solution would have been:

Suppose that that the number of noses was x. You know that 9120 is 14% too high, that is 9120 is 100% of x plus 14% of x, in other words 114% of x. Thus
9120 = ¹¹⁴/₁₀₀ x
and hence x = 9120 ¹⁰⁰/₁₁₄ = 8000

Using the same argument "128% too high" gives

x = 9120 ¹⁰⁰/₂₂₈ = 4000 Maybe what is expected is x = 9120 ¹⁰⁰/₁₂₈ = 7125 In your opinion, which of these calculations corrects a count that is "128 percent too high"?

Cheers,
Claude Go to Math Central