Respuesta :
x = amount invested at 14%
4x = amount invested at 5.5%, 4 times as "x".
[tex]\bf \begin{array}{|c|ll} \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}~\hfill \stackrel{\textit{14\% of x}}{\left( \cfrac{14}{100} \right)x}\implies 0.14x~\hfill \stackrel{\textit{5.5\% of 4 times x}}{\left( \cfrac{5.5}{100} \right)4x}\implies 0.22x \\\\[-0.35em] ~\dotfill[/tex]
[tex]\bf 0.14x+0.22x~~=~~\stackrel{\textit{total annual yield}}{550}\implies 0.36x=550 \\\\\\ x=\cfrac{550}{0.36}\implies \stackrel{\textit{invested at 14\%}}{x=1527.\overline{7}}~\hfill \stackrel{\textit{invested at 5.5\%}}{4(1527.\overline{7})\approx 6111.11}[/tex]
Account A earns at a 5.5% interest rate
Account B earns at a 14% interest rate
We want to invest 4 times as much in account A compared to account B
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Let x be the amount invested in account B. So the amount invested in account A is 4x.
Use the simple interest formula, i = P*r*t, to find that
interest earned with account A = 4x*0.055*1 = 0.22x
interest earned with account B = x*0.14*1 = 0.14x
Add these up and set this equal to 550. Solve for x. Then compute 4x.
0.22x+0.14x = 550
0.36x = 550
x = 550/0.36
x = 1527.77777777778
x = 1527.78 round to the nearest penny
4x = 4*1527.78
4x = 6111.12
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Answers:
6111.12 dollars needs to be invested at 5.5%
1527.78 dollars needs to be invested at 14%
