Systems of linear equations word problems 1. The owner owner of a landsca landscaping ping company company is develop developing ing a proposal proposal to to maintain maintain the grounds grounds of of a building. It is estimated that 75 gardening hours and 25 foreman hours will be required. The total budget for these hours is 1!"". The hourly wage for a foreman is #"$ more than a gardener plus an additional 1.!5 per hour. %hich of the following systems of equations can be used to determine the hourly wages of a gardener& g& and a foreman& f& so the total wages are 1!""' (. 25g) 25g)75 75f* f*1! 1!"" "" f*1.#g)1.!5 +. 25f 25f)75g )75g* *1!" 1!"" f*1.#g)1.!5 ,. 25g) 25g)7 75f* 5f*1!" 1!"" g*1.#f)1.!5 -. 25f) 25f)75 75g* g*1! 1!"" "" g*1.#f)1.!5 ,orrect answer + -ifficulty level 2 2. -evin -evin is a landsca landscaper per who needs needs to prepar preparee differ different ent types types of grass grass seed seed for his custome customers/ rs/ yards. +luegrass seed costs 2."" per pound while drought0resistant seed costs #."" per pound. If for a particular day the two types of grass seed totaled !."" and together weighed 25 pounds& how many pounds of bluegrass seed did -evin prepare' (. pounds of of bluegrass bluegrass seed seed and 21 pounds pounds of drought0 drought0resi resistant stant seed seed +. 7 pounds of of bluegrass bluegrass seed seed and 1 pounds pounds of drought0 drought0resi resistant stant seed seed ,. 1 pounds pounds of bluegrass bluegrass seed seed and and 7 pounds of drought0 drought0resi resistant stant seed seed -. 21 pounds pounds of bluegrass bluegrass seed seed and and pounds of drought0 drought0resi resistant stant seed seed ,orrect answer answer + -ifficulty level 2 #.
3icardo 3icardo had two two types of homewor homewor4 4 assignments assignments for his his college college math class. class. The The amount amount of mmm mini assignments he had was one fewer than twice the amount of l long long assignments he had. If he had a total of ! mini and long assignments& which of the following systems of equations can be used to find out how any mini and long assignments he had' (. m*2l 1 1 m)l *! *! +. m*2l 1 1 m*l )! )! ,. l *2m1 *2m1 m)l *! *! -. l *2m1 *2m1 m*l )! )! ,orrect answer ( -ifficulty -ifficult y level 2
. 6ne Satur Saturday day&& a butche butcherr sells meat meat at a local local farmer/s farmer/s mar4et mar4et and ma4es ma4es a total number number of dollars from selling a specific number of pounds of beef at !.""!.""!."" per pound as well as 7.""7.""7."" from selling por4. 6n Sunday& she ma4es the same amount of money from selling an equivalent bbb pounds of beef at ."".""."" per pound as well as 5.""5.""5."" from selling por4. %hich system of equations can be used to find out how many bbb pounds of beef she made for a total of ddd dollars' (. d*b)7 d*!b)5 +. d*!b)7 d*b)5 ,. b*d)7 b*!d)5 -. b*!d b*!d)7 )7 b*d b*d)5 )5
,orrect answer answer + -ifficulty level 2 5. ( piec piecee of glass glass with with an initi initial al tempe temperat ratur uree of 88 , is cooled at a rate of #.5 , per minute. ,oncurrently& a piece of copper with an initial temperature of " , is heated at 2.5 , per minute. %hich of the following systems of equations can be used to solve for the temperature& T& in degrees ,elsius& and the time& m& in minutes& when the glass and copper reach the same temperatures' (. T*88)#.5m T*2.5m +. T*88#.5m T*2.5m ,. T*88)2.5m T*#.5m -. T*882.5m T*#.5m ∘
∘
∘
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,orrect answer answer + -ifficulty level 2 !.
( vegeta vegetable ble stand stand sells p pump4ins pump4ins for for 5."" each each and s squashes squashes for for #."" #."" each. 6n 9onday 9onday&& the stand sold ! more squashes than pump4ins and made a total of 8."". %hich system of equations can be used to determine the number of pump4ins and squashes sold' (. #p)5s p)5s* *8 s*p)! +. #p)5s*8 p*s)! ,. 5p)#s*8 s*p)! -. 5p)#s p)#s* *8 p*s)! ,orrect answer answer , -ifficulty level #
7.
9i4ayla 9i4ayla is the communica communications tions director director for for a politician politician and has has recommend recommended ed that a total total of 1 tal4s are given by the politician before election day. She also recommends recommends a total of 8 more formal speeches& s& than informal tal4s& t. %hich of the following systems of equations can be used to find out how many formal speeches versus informal tal4s she had' (. t*s)8 s)t*1 +. t*s)8 s*t1 ,. s*t)8 s)t*1 -. s*t)8 s*t1 ,orrect answer answer , -ifficulty level #
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Tic4ets Tic4ets for for a concert concert were 5 for for each each child and and for each each adult. (t one of of the concerts& concerts& each each adult brought children with them& and 1" children attended without an adult. The total tic4et sales were 17#". %hich of the following systems of equations can be solved to determine the number of children& c& and adults& a& who attended the concert' (. 5c) 5c)a* a*17#" 17#" a)1"*c +. 5c) 5c)a* a*17#" 17#" a1"*c ,. c) c)5a* 5a*17#" 17#"
a)1"*c -. c) c)5a* 5a*17#" 17#" a1"*c ,orrect answer ( -ifficulty -ifficult y level # 8.
Today Today&& the populati population on of ,anyon ,anyon :alls is 22&5"" 22&5"" and the populatio population n of Swift ,ree4 ,ree4 is 15&2"". 15&2"". The population population of ,anyon ,anyon :alls is decreasi decreasing ng at the rate of 7" people each year while the population of Swift ,ree4 is increasing at the rate of 1&5"" each year. (ssuming (ssuming these rates continue into the future& in how many years from today will the population of Swift ,ree4 equal twice the population of ,anyon :alls' (. 8 years +. 1" ye years ,. 11 years -. 12 years ,orrect answer answer + -ifficulty level #
1". The owner owner of a health health food store is developing developing a new product that consists consists of peanuts and raisins. 3aisins cost 2.5" per pound and peanuts cost #.5" per pound. The owner wants to create 2" pounds of the product that cost #."# per pound. %hich of the following systems of equations equations can be used to determine the number of pounds of peanuts& peanuts& p& and the number number of pounds of raisins& r& r& that should be combined' combined' 2.50 p + 3.50 r
(.
p−r = 20
+.
p + r =20
,. -.
p−r = 20 2.50 2.50 p + 3.50 r = 3.03
20
2.50 p + 3.50 r 20
= 3.03
= 3.03
p + r =20 2.50 2.50 p + 3.50 r =3.03
,orrect answer answer + -ifficulty level # 11. ;erry ;erry has a large car which which holds 22 gallons gallons of fuel and get 2" miles per gallon. gallon.
ers e?pect to sell all of the tic4ets& and they want to collect 1&85" from the tic4et sales. %hich of the following systems of equations can be used to determine the price& p& of each premium tic4et and the price& r& of each regular tic4et'
(. 5"p) 5"p)12 125r 5r*1 *185 85" " p1.25r*1.5" +. 5"p) 5"p)12 125r 5r*1 *185 85" " p1.5"r*1.25 ,. 125p 125p)5 )5"r "r*1 *185 85" " p1.25r*1.5" -. 125p 125p)5 )5"r "r*1 *185 85" " p1.5"r*1.25 ,orrect answer ( -ifficulty -ifficult y level 1. The length length of a rectangu rectangular lar swimming swimming pool is twice the width. If the perimeter perimeter is 12" feet& then what is the width in feet' feet ,orrect answer answer 2" -ifficulty level level 15. :or a high school dinner function function for teachers teachers and students& students& the math department department bought ! cases of @uice and 1 case of bottled water for a total of 1#5. The science department bought cases of @uice and 2 cases of bottled water for a total of 11". Aow much did a case of @uice cost' (. 12.5" +. 15."" ,. 2"."" -. 25."" ,orrect answer answer , -ifficulty level