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mash [69]
3 years ago
5

janice invests a total of 8000 in two different accounts. the first account returns 5%, while the second account returns 8%. if

the total interest earned after one year is 565, what principal did she invest in each account?​
Mathematics
1 answer:
Zinaida [17]3 years ago
6 0

Answer:

"She invested $2500 in 5% account and $5500 in 8% account"

Step-by-step explanation:

Let the amount invested in 5% account be "x"

So, the amount invested in 8% account would be "8000 - x"

Interest amount is the percentage multiplied by amount invested. So

Interest of 5% account = 5% of x = 0.05x

Interest of 8% account = 8 % of 8000 - x = 0.08(8000 - x)

Total interest is the sum of these 2 expressions that EQUATES to 565 (given). Let's solve for x:

0.05x + 0.08(8000 - x) = 565\\0.05x+640-0.08x=565\\0.03x=75\\x=2500

and thus,

"8000 - x" = 8000 - 2500 = 5500

Hence,

She invested $2500 in 5% account and $5500 in 8% account

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c.

\frac{5}{4} x - 2 = \frac{3}{2} x-4

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\frac{5}{2} x +\frac{7}{2} =\frac{3}{4} x+14 \\\frac{5}{2}x -\frac{3}{4} x=14-\frac{7}{2} \\\frac{10-3}{4} x =\frac{28-7}{2} \\\frac{7}{4} x =\frac{21}{2} \\x = \frac{21}{2} * \frac{4}{7} = 6 \\

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\frac{5}{4} x -9 = \frac{3}{2} x-12 \\\frac{5}{4} x - \frac{3}{2} x= -12 + 9 \\\frac{5-6}{4} x = -3 \\\frac{-1}{4} x = -3 \\x = -3 * -4 \\x = 12

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\frac{5}{4} x-2=\frac{3}{2} x-4 \\\frac{5}{4} x-\frac{3}{2} x=-4+2 \\\frac{5-6}{4}x=-2 \\\frac{-1}{4} x = -2 \\x = -2 * -4 \\x = 8

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You could also replace x for 8 in every equation and see if both sides give the same answer

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