Mathematics: Awoman has money in two accounts. one account pays 5% annual interest, whereas the other pays 10% annual interest. if she has $800 more invested in 10% than she does at 5% and her total interest for a year is $250, how much does she have in each account?

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Awoman has money in two accounts. one account

ShayMoore

10.01.2022

She have $1133.33 in account which pays 5% annual interest and he have $1933.33 in account which pays 10% annual interest

Step-by-step explanation:

Let x be the amount she invested at 5% annual interest

She invested $800 more in 10%

So, she invested x+800 at 10% annual interest

Case 1:

Principal = x

Time = 1 year

Rate of interest = 5%

$Si =\frac{P \times R \times T}{100}$

$SI=\frac{x \times 5 \times 1}{100}$

$SI=\frac{5}{100}x$

Case 2:

Principal = x+800

Time = 1 year

Rate of interest = 10%

$Si =\frac{P \times R \times T}{100}$

$SI=\frac{(x+800) \times 10 \times 1}{100}$

$SI=\frac{10}{100}(x+800)$

Interest = Amount - principal = 880+1.1x-x=880+0.1x

Her total interest for a year is $250

So, $\frac{5}{100}x+\frac{10}{100}(x+800)=250$

$\frac{5}{100}x+\frac{10}{100}(x+800)=250$

$\frac{5}{100}x+\frac{10}{100}x+80=250$

$\frac{15}{100}x+80=250$

$\frac{15}{100}x=250-80$

$x=170 \times \frac{100}{15}$

x=1133.33

So the amount she invested at 5% annual interest is $1133.33

She invested at 10% annual interest=x+800=1133.33+800=1933.33

Hence she have $1133.33 in account which pays 5% annual interest and he have $1933.33 in account which pays 10% annual interest

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