SOLUTION: If someone can help explain these two word problems in explicit detail I would greatly appreciate it!!!! 1. Donna invested her $33,000 bonus and received a total of $970 in int

Algebra ->  Algebra  -> Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: If someone can help explain these two word problems in explicit detail I would greatly appreciate it!!!! 1. Donna invested her $33,000 bonus and received a total of $970 in int      Log On

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Question 120493This question is from textbook
: If someone can help explain these two word problems in explicit detail I would greatly appreciate it!!!!
1. Donna invested her $33,000 bonus and received a total of $970 in interest after one year. If part of the money returned 4% and the remainder 2.25%, then how much did she invest at each rate?


2. Tickets for a concert were sold to adults for $3 and to students for $2. If the total receipts were $824 and twice as many adult tickets as student tickets were sold, then how many of each were sold? This question is from textbook

Answer by stanbon(48575) About Me  (Show Source):
You can put this solution on YOUR website!
1. Donna invested her $33,000 bonus and received a total of $970 in interest after one year. If part of the money returned 4% and the remainder 2.25%, then how much did she invest at each rate?
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Let amt. at 4% be "x" ; interest on this is 0.04x dollars
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Amt at 2.25% is "33000-x" ; interest is 0.0225(33000-x)= 742.50-0.0225x dollars
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EQUATION:
interest + interest = 970 dollars
0.04x + 742.50-0.0225x = 970
0.0175x = 227.50
x = 13000 (amt invested at 4%)
33000-x = 20000 (amt invested at 2.25%)
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2. Tickets for a concert were sold to adults for $3 and to students for $2. If the total receipts were $824 and twice as many adult tickets as student tickets were sold, then how many of each were sold?
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Let # of adult tiks sold be "2x" ; value = 3*2x = 6x dollars
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# of stud tiks sold is "x" ; value is 2x dollars
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EQUATION:
value + value = 824
6x + 2x = 824
8x = 824
x = 103 (# of student tickets sold)
2x = 206 (# of adult tickets sold)
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Cheers,
Stan H.