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02.03.2021 •
Mathematics
Two investments totaling $37,500 produce an annual income of $2210. One investment yields 6% per year, while the other yields 5% per year. How much is invested at each rate?
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Ответ:
a = $33,500 at 6%
b = $4,000 at 5%
Detailed
37,500 = a + b
b = 37,500 - a
a = 37,500 - b
2,210 = a*6% + b*5%
2,210 = a*6% + 5%*(37,500 - a)
2,210 = a*6% - a*5% + 37,500*5%
2,210 = a*(6% - 5%) + 1,875
335 = a*( 6/100 - 5/100)
335 = a*( 1/100)
a = (335*100)/1
a = $33,500
b = 37500 - a
b = 37500 - 33500
b = 4000
Plug back in to check if the amounts invested at each rate equal $2210:
$2210 = a*6% + b*5%
$2210 = 33500*6% + 4000*5%
$2210 = $2010 + $200
$2210 = $2210
Ответ: