word problem, can't figure out where to start

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a depth finder shows that the water is a certain place is 620 feet deep. the difference between d, the actual depth of the water and the reading is the absolute value of d-620, and must be less than or equal to 0.05d. Find the minimum and maximum values of d, to the nearest tenth of a foot.

how on earth do I find the minimum and maximum values? algebraically?
 
If \(\displaystyle \mbox{|d - 620| \leq 0.05d}\),

\(\displaystyle \mbox{ }\)then \(\displaystyle \mbox{(d - 620) \leq 0.05d }\) or \(\displaystyle \mbox{ -(d - 620) \leq 0.05d}\).

Notice that the latter is equivalent to (divide both sides by -1 and hence change the direction of the inequality) \(\displaystyle \mbox{d - 620 \geq 0.05d}\).
 
You could solve it algebraicly or graphically
d-620< 0.5d
.5d-620=0
.5d=620
d= 1240
i think thats how you find the max
 
Sorry, my last inequality should read \(\displaystyle \mbox{d - 620 \geq -0.05d}\).
 
Yeah, I found that mistake myself.

The answer comes out to be that the max is 652.6 and the min is 509.5 (rounded to the nearest tenth), right?
 
Your max is good but your min is dodgy (|509.5 - 620| = 110.5 which is greater than 0.05*509.5=25.5).

I can't see where your error is unless you show your work.

(To impress your teacher, you might consider how the max and min each should be rounded, as opposed to just to the nearest foot.)
 
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