Number of Solutions
5x-4=5x+4
-4=4
False
No Solution
x2-61=300
x=19,-19
cbrt{x-1}=10
x=1001
WRITE AN EQUATION AND ANSWER THE QUESTION:
A pipet is a scientific instrument used to drip water into a container. One pipet in particular forms drops that are 0.1 mL per drop. How many drops will it take to fill a 10 mL beaker?
EQUATION: 0.1d=10
SOLUTION: d=100 drops
ANSWER: It takes 100 drops to fill a 10 mL beaker.
WRITE AN EQUATION AND ANSWER THE QUESTION:
Pam makes $15 an hour. Melissa makes $10 dollars an hour. How many hours will it take for their wages to be the same?
EQUATION: 15h = 10h
SOLUTION: m= 0 hours
ANSWER: Their wages will never be the same.
20x-34x=-14x+3
0=3
False
No Solution
sqrt{x+7}=4
x=9
x3-27=0
x= 3
WRITE AN EQUATION AND ANSWER THE QUESTION:
A student has an unfinished quiz that she has to complete. She already has 5 questions completed and can answer questions at a constant rate of 2 questions per minute. If there are a total of 25 questions left on the test, how long will it take for her to finish?
EQUATION: 5+2t=25
SOLUTION: t=10 minutes
ANSWER: It will take her 10 minutes to complete the quiz.
WRITE AN EQUATION AND ANSWER THE QUESTION:
Billy's Barbecue pays their waiters $9 per hour plus tips. One night, their waiter Kevin received a total of $15 in tips. Conner's Cakes pays their baker Stella $10.50 per hour. How many hours will Stella have to work in order to make the same amount as Kevin that one night?
EQUATION: 9m+15=10.50m
SOLUTION: 10 hours
ANSWER: Stella will have to work 10 hours in order to make the same amount of money as Kevin that night.
(2+5)x=6x-12
x=-12
One Solution
sqrt{2x-7}=9
x=44
x3+200=-312
x= -8
WRITE AN EQUATION AND ANSWER THE QUESTION:
Charlie doesn't know how to shop. He buys the same number of lemons from two different stores. One store sells them at $1 per lemon, and the other sells them at $3 per lemon. If his total came out to be $36, how many lemons did he buy?
EQUATION: L+3L=36
SOLUTION: L=9
ANSWER: Charlie bought 18 lemons.
WRITE AN EQUATION AND ANSWER THE QUESTION:
Jen takes a group fo kids to the movies. Tickets were $8 for children and $10 for adults. She then buys each kid a bag of popcorn which was $3 per bag. The next day, she takes them to the mall and buys $1 water guns for each child and one bag of water balloons for $20. If she spends the same amount of money each day, how many children were with Jen?
EQUATION: 8c+10+3c=c+20
SOLUTION: c = 2 children
ANSWER: Jen had 2 children with her.
2(5x-13)=20x-20-10x-6
-26=-26
True
Infinitely many solutions OR All real numbers
-2(x-7)2+17=-631
x=-18,25
(2x-7)3+26=27
x=4
WRITE AN EQUATION AND ANSWER THE QUESTION:
A standard oil change at Marvin's Mechanics costs a service charge of $30 plus $5 per gallon; however, Carl Sherman's Car Shop costs twice as much as Marvin's Mechanics. If I spent $75 on an oil change at Carl Sherman's, how many gallons of oil did my car take?
EQUATION: 2(30+5g)=75
SOLUTION: g=1.5 gallons
ANSWER: Your car takes 1.5 gallons of oil.
WRITE AN EQUATION AND ANSWER THE QUESTION:
There is miscommunication at Jim's workplace. He has two bosses. One boss pays him $7 per hour while unknowingly the other boss pays an additional him $9.50. Eventually they realize their mistake, so they giving Jim $50 for the inconvenience plus $8.25 per hour. Approximately how many hours does Jim have work to make the same amount?
EQUATION: 7h+9.50h = 50+8.25h
SOLUTION: h=6 hours
ANSWER: Jim has to work roughly 6 hours to make the same pay.
2(-3x+1)-12=5(2x+1)-4x+3
x=-1.5
One Solution
3(5x-4)2-1900=128
x= -4.4, 26
Give and exact solution:
x3-9=0
x= cbrt{9} or 2.0800828...
WRITE AN EQUATION AND ANSWER THE QUESTION:
Victor's Violins sells violins with a mandatory insurance policy of $25 dollars. Irene's Instruments sells violins at half the cost of Victor's plus $30. If I buy a violin at Irene's for $92.50, how much does Victor price his violin's?
EQUATION: 0.5(v+25)+30=92.50
SOLUTION: v=$100
ANSWER: Victor prices his violins at $100.
WRITE AN EQUATION AND ANSWER THE QUESTION:
Jim, Joe, and Phil are at it again. This time, they are talking about how many golf clubs they have. Jim has a third of the amount of Joe and Phil put together where Phil has 36 golf club. In other words, Jim has twice the amount of Joe plus 1 more. How many golf clubs does Joe have?
EQUATION: 1/3 * (j+36) = 2j+1
SOLUTION: j = 4 golf clubs
ANSWER: Joe has 4 golf clubs.