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- A collection of dimes and quarters is worth S15.25. There are 103 coins in all. How many of each is there? ሺെ10ሻሺ ܦܳ ሻ ൌ ሺ103ሻሺെ10ሻ 10 ܦ 25 ܳൌ 1525 െ10 ܦെ 10 ܳൌ െ ଵହொ ଵହ ൌ^
ସଽହ ଵହ ܦ 33 ൌ 103 ܳൌ 33 െ33 െ 33 ܦൌ 70 ݏ ݁݉݅݀ 70 ݏݎ݁ݐݎܽݑ ܳ 33
- The attendance at a school concert was 578. Admission was $2.00 for adults and $1.50 for children. The total receipts were S985.00. How many adults and how many children attended? െ2ሺ ܣ ܥሻ ൌ ሺ578ሻሺെ2ሻ 2 ܣ 1.5 ܥൌ 985 െ2 ܣെ 2 ܥൌ െ ି.ହି .ହ ൌି^
ଵଵହି .ହ ܣ 342 ൌ 578 ܥൌ 342 െ342 െ 342 ܣൌ 236 ݏݐ݈ݑ݀ܣ 236 ݊݁ݎ݈݄݀݅ܥ 342
- A boy has $2.25 in nickels and dimes. If there are twice as many dimes as nickels, how many of each kind has he? 5 ܰ 20 ܰൌ 225 ଶହே ଶହ ൌ^
ଶଶହ ଶହ ݏ ݈݁݇ܿ݅ܰ 9 ܰൌ 9 ݏ݁݉݅ܦ 18 ܦൌ 2ሺ9ሻ ൌ 18
- A collection of 27 coins consisting of nickels and dimes amounts to $2.25. How many coins of each kind are there? ሺെ10ሻሺ ܰ ܦ ሻ ൌ ሺ27ሻሺെ10ሻ 5 ܰ 10 ܦൌ 225 െ10 ܰെ 10 ܦൌ െ ିହேି ହ ൌି^
ସହି ହ ܰൌ 9 9 ܦൌ 27 െ9 െ 9 ݏ݁݉݅ܦ 18 ܦൌ 18 ݏ ݈݁݇ܿ݅ܰ 9
N V T
D 10 10D
Q 25 25Q
N V T
A 2 2A
C 1.5 1.5C
N V T
N 5 5N
D=2N 10 20N
N V T
N S SN
D 10 10D
- There were 429 people at a play. Admission was $1 each for adults and 75 cents each for children. The receipts were $372.50. How many children and how many adults attended? ሺെ1ሻሺ ܣ ܥሻ ൌ ሺ429ሻሺെ1ሻ ܣ .75 ܥൌ 372. ܥ െ ܣെ ൌ െ ି.ଶହି .ଶହ ൌି^
ହ.ହି .ଶହ ܣ 226 ൌ 429 ܥൌ 226 െ226 െ 226 ܣൌ 203 ݏݐ݈ݑ݀ܣ 203 ݊݁ݎ݈݄݀݅ܥ 226
- There were 203 tickets sold for a volleyball game. For activity‐card holders, the price was $1. each and for non‐card holders the price was $2 each. The total amount of money collected was $310. How many of each type of ticket was sold? െ2ሺ ܣܰ ሻ ൌ ሺ203ሻሺെ2ሻ 1.25 ܣ 2 ܰൌ 310 െ2 ܣെ 2 ܰൌ െ ି.ହି .ହ ൌି^
ଽି .ହ 128 ܰൌ 203 ܣൌ 128 െ128 െ 128 ܰൌ 75 ݀ݎܽܥ ݊ ܰ 75 ݀ݎܽܥ ݕݐ݅ݒ݅ݐܿܣ 128
- At a recent Vikings game $445 in admission tickets was taken in. The cost of a student ticket was $1.50 and the cost of a non‐student ticket was $2.50. A total of 232 tickets were sold. How many students and how many nonstudents attended the game? െ1.5ሺ5 ܰ ሻ ൌ ሺ232ሻሺെ1.5ሻ 1.55 2.5 ܰൌ 445 െ1.55 െ 1.5 ܰൌ 348 ܰൌ 97 ܵ 97 ൌ 232 െ97 െ 97 ݏݐ݊݁݀ݑݐ ܵെ ݊ ܰ 97 ܵൌ 135 ݏݐ݊݁݀ݑݐ ܵ 135
N V T
A 1 A
C .75 .75C
N V T
A 1.25 1.25A
N 2 2N
N V T
N 2.5 2.5N
- A total of $27000 is invested, part of it at 12% and the rest at 13%. The total interest after one year is $3385. How much was invested at each rate? െ.12ሺ ݔ ݕሻ ൌ ሺ27000ሻሺെ.12ሻ ݔ 14500 ൌ 27000
. 12 ݔ .13 ݕൌ 3385 െ14500 െ 14500 െ.12 ݔെ .12 ݕൌ െ3240 ݔൌ 12500 ି.ଵ௬ି .ଵ ൌି^
ଵସହି .ଵ ݕൌ 14500 $12,500 @12% $14,500 @ 13%
- A total of $9000 is invested, part of it at 10% and the rest at 12%. The total interest after one year is $1030. How much was invested at each rate? െ.1ሺ ݔ ݕሻ ൌ ሺ9000ሻሺെ.1ሻ ݔ 6500 ൌ 9000
. 1 .12 ݕൌ 1030 െ6500 െ 6500 െ.1 ݔെ .1 ݕൌ െ900 ݔൌ 2500 .ଶ௬ .ଶ ൌ^
ଵଷ .ଶ ݕൌ 6500 $2500 @ 10% $6500 @ 12%
- An inheritance of $10000 is invested in 2 ways, part at 9.5% and the remainder at 11%. The combined annual interest was $1038.50. How much was invested at each rate? െ.095ሺ ݔ ݕሻ ൌ ሺ10000ሻሺെ.095ሻ ݔ 5900 ൌ 10000
. 095 ݔ .11 ݕൌ 1038.50 െ5900 െ 5900 െ.095 ݔെ .095 ݕൌ െ950 ݔൌ 4100 .ଵହ௬ .ଵହ ൌ଼଼^
.ହ .ଵହ ݕൌ 5900 $4100 @ 9.5% $5900 @11%
- Jason earned $256 interest last year on his investments. If $1600 was invested at a certain rate of return and $2400 was invested in a fund with a rate that was double the rate of the first fund, find the two rates of interest. 1600 ݔ 4800 ݔൌ 256 ସ௫ ସ ൌ^
ଶହ ସ ݔൌ 0.04 $1600 @ 4% 2 ݔൌ 0.08 $2400 @ 8%
N V T
x .12 .12x y .13 .13y 27000 3385
N V T
x .10 .1x y .12 .12y 9000 1030
N V T
x .095 .095x y .11 .11y 10000 1038.
N V T
1600 x 1600x 2400 2x 4800x 256
- A total of $8500 is invested, part of it at 6% and the rest at 3.5%. The total interest after one year is $385. How much was invested at each rate? െ.035ሺ ݔ ݕሻ ൌ ሺ8500ሻሺെ.035ሻ 3500 ݕൌ 8500 .06 ݔ .035 ݕൌ 385 െ3500 െ 3500 െ.035 ݔെ .035 ݕൌ െ297.5 ݕൌ 5000 .ଶହ௫ .ଶହ ൌ଼^
.ହ .ଶହ ݔൌ 3500 $3500 @ 6% $5000 @ 3.5%
- A total of $15000 is invested, part of it at 8% and the rest at 11%. The total interest after one year is $1455. How much was invested at each rate? െ.08ሺ ݔ ݕሻ ൌ ሺ15000ሻሺെ.08ሻ ݔ 8500 ൌ 15000
. 08 ݔ .11 ݕൌ 1455 െ8500 െ 8500 െ.08 ݔെ .08 ݕൌ െ1200 ݔൌ 6500 .ଷ௬ .ଷ ൌ^
ଶହହ .ଷ ݕൌ 8500 $6500 @ 8% $8500 @ 11%
- A total of $6000 is invested, part of it at 4.25% and the rest at 5.75%. The total interest after one year is $300. How much was invested at each rate? െ.0425ሺ ݔ ݕሻ ൌ ሺ6000ሻሺെ.0425ሻ ݔ 3000 ൌ 6000 .0425 ݔ .0575 ݕൌ 300 െ3000 െ 3000 െ.0425 ݔെ .0425 ݕൌ െ255 ݔൌ 3000 .ଵହ௬ .ଵହ ൌ^
ସହ .ଵସ ݕൌ 3000 $3000 @ 4.25% $3000 @ 5.75%
- A total of $11000 is invested, part of it at 6.8% and the rest at 8.2%. The total interest after one year is $797. How much was invested at each rate? െ.068ሺ ݔ ݕሻ ൌ ሺ11000ሻሺെ.068ሻ ݔ 3500 ൌ 11000
. 068 ݔ .082 ݕൌ 797 െ3500 െ 3500 െ.068 ݔെ .068 ݕൌ െ748 ݔൌ 7500 .ଵସ௬ .ଵସ ൌ^
ସଽ .ଵସ ݕൌ 3500 $7500 @ 6.8% $3500 @8.2%
N V T
x .06 .06x y .035 .035y 8500 385
N V T
x .08 .08x y .11 .11y 15000 1455
N V T
x .0425 .0425x y .0575 .0575y 6000 300
N V T
x .068 .068x y .082 .082y 11000 797
