document.write( "Question 817797: Sam invested $1950, part of it at 6% and the rest at 8% yearly interest. the yearly income on the 8% investment was $6 more than twice the income from 6% investment. How much did he invest at each rate?
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Algebra.Com's Answer #492202 by FightinBlueHens(27)\"\" \"About 
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Sam divided the his money into 2 parts. Together they equal $1,950, so if one part is x, and the other part is y, then x + y = 1,950.
\n" ); document.write( "Because you have 2 variables, you need 2 equations to solve the problem. Above you have the first equation, but you can't solve it on it's own, so you need the second one to help you.
\n" ); document.write( "We know that the first one has an 8% yield, the second one has a 6% yeild, and the yield of the first one $6 more than twice the profit of the second amount, so you need to represent in an equation.
\n" ); document.write( "Use 1.08 and 1.06 for the yield because recieves interest, but also keeps the amount he started out with, so the equation will be 1.08x = 2(1.06y) + 6
\n" ); document.write( "First distribute: 1.08x = 2.12y + 6
\n" ); document.write( "Write these steps out on your paper and write the values as decimals, mixed fractions or imporper fractions so you don't get confused. I will show you all 3.
\n" ); document.write( "Then you want to get 1 variable on one side, so I'll do this for x: x = (2.12y + 6)/1.08
\n" ); document.write( "2.12/1.8 = 1.9629... but it's not an irrational number, it is equal to 1 + 26/27 (1 and 26/27) which is 53/27
\n" ); document.write( "6/1.08 = 5.555555... or 5 + 5/9 (5 and 5/9) or 49/9
\n" ); document.write( "x = (53/27)y + 49/9 = 53y/27 + 5.55 OR 53y/27 + 49/9
\n" ); document.write( "Substitute this value for x in the first equation (x + y = 1950): 53y/27 + 5.55 + y = 1950
\n" ); document.write( "Remember: y = 1y, and any number diveded by itself equals 1
\n" ); document.write( "multpily y by 27/27 to add this to the 54y/27, so this will be: 53y/27 + 27y/27
\n" ); document.write( "Add the neumerators (the denomeinator stays the same): 53 + 27 = 80,
\n" ); document.write( "so 53y/27 + 27y/27 = 80y/27\r
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\n" ); document.write( "\n" ); document.write( "Now you have: 80y/27 + 5.55 = 1950
\n" ); document.write( "Subtract 5.55 from both sides: 80y/27 = 1944.44
\n" ); document.write( "Multiply both sides by 27 to cancel out the denominator and you get: 27(80y/27)= 1944.44*27
\n" ); document.write( "which equals: 80y = 52,500
\n" ); document.write( "Divide both sides by 80 to cancel out the 80 on the left hand side and to solve for y: y = 52,500/80
\n" ); document.write( "which makes y equal to 656.25\r
\n" ); document.write( "\n" ); document.write( "This is how much he invested in the 6% yield option, so to figure out the other part of his investment, subtract this amount from the original amount ($1950): 1950 - 656.25 = 1,293.75\r
\n" ); document.write( "\n" ); document.write( "Check your work: substitute x and why in the second equation to make sure that they work:
\n" ); document.write( "1.08x = 2(1.06y) + 6
\n" ); document.write( "1.08(1,293.75) = 2(1.06* 656.25) + 6
\n" ); document.write( "1,397.25 = 2(1.06*656.25) + 6
\n" ); document.write( "1,397.25 = 2(695.625) = 6
\n" ); document.write( "1,397.25 = 1,391.25 + 6
\n" ); document.write( "1,397.25 = 1,397.25
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