The Coopers have an orange juicer that they use to make fresh squeezed OJ. THe first squeezing the juicer extracts 1/3 of the total juice in the oranges. Each succeeding squezzing extracts about 1/3 of the remaining juice. How long will it take to get at least 3/4 of the orange's juice? How many squeezings will it take to get at least 9/10 of the juice?
Math Word Problem Question Can't figure it out?
- Thread starter dusty
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It appears to be far easier to ponder how much it DOESN'T squeeze.dusty said:
If is squeezes 1/3, it leaves 2/3
1 Squeeze 2/3
2 Squeezes (2/3)*(2/3) = 4/9 = .44444444 -- Over half gone.
3 Squeezes (4/9)*(2/3) = 8/27 = 0.296... -- Not quite 3/4 gone
If it has squeezed 3/4, the orange has retained 1/4, then (2/3)<sup>x</sup> = 1/4 ==> x = 3.419, so four squeezes ar required.
Similarly, (2/3)<sup>x</sup> = 1/10 ==> x = what? You tell me.
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What?
(2/3)<sup>x</sup> = 1/10
Have you met logarithms?
x*log(2/3) = log(1/10)
x = -log(10)/log(2/3) = -1/(-0.1761) = 5.68 <== So it takes 6 squeezes.
If you haven't met logarithms,
(2/3)<sup>4</sup> = 0.1975 -- Just over 80% gone.
(2/3)<sup>5</sup> = 0.1317 -- Not quite 90% gone.
(2/3)<sup>6</sup> = 0.0878 -- There it is. More than 90% gone.
(2/3)<sup>x</sup> = 1/10
Have you met logarithms?
x*log(2/3) = log(1/10)
x = -log(10)/log(2/3) = -1/(-0.1761) = 5.68 <== So it takes 6 squeezes.
If you haven't met logarithms,
(2/3)<sup>4</sup> = 0.1975 -- Just over 80% gone.
(2/3)<sup>5</sup> = 0.1317 -- Not quite 90% gone.
(2/3)<sup>6</sup> = 0.0878 -- There it is. More than 90% gone.