Please assist me with the following word problem: A local group of scouts has be

Question

Please assist me with the following word problem:
A local group of scouts has been collecting old aluminum cans forrecycling. The group of scouts has already collected 12,000lb of cans, for which they could currently receive $4 per hundredpounds. The group can continue to collect cans at the rate of400 lb per day. However, a glut in the old-can market hascaused the recycling company to announce that it will lower itsprice, starting immediately, by $.10 per hundred pounds perday. The scouts can make only one trip to the recyclingcenter. How many days should they wait in order to get $490for their cans?

Thanks!

Explanation / Answer

d = (12000+400t)(4-.1t)/100 = 490
Multiply through and put them all to one side to get: -.4 t^2 + 4t - 10 = 0
Multiply by -2.5 to get whole numbers t^2 -10t + 25 = 0
Factor to get: (t-5)(t-5) = 0
Solve using the quadratic equation or just set the factors equal to0 to find that t = 5 days is when they would get $490 (set equationequal to 0)
Hope that helps

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