Word Problems Flashcards
Exponent Word Problems:
Carbon-14 is a radioactive element that decays to 1/2 or 2-1, of its original amount after every 5 700 years. Determine the remaining mass of 10 g of Carbon-14 after:
a) 11 400 years
b) 28 500 years
1) Divide the number of years in a and b by the number of years it takes for the material to decay
a) 11 400/5 700= 2
b) 28 500/5 700= 5
2) Take the amount of the material you currently have, and divide it by the amount it decays as many times as the answer in the previous step
a) 10/2 (Half) 2 times
10/2= 5, 5/2= 2.5
b) 10/2 (Half) 5 times
10/2=5, 5/2=2.5, 2.5/2= 1.25, 1.25/2= 0.625, 0.625/2= 0.3125
Therefore, in 11 400 years there will be 2.5 g left, and in 28 500 years there will be 0.3125g left.
A flight from London to Halifax which is 1 420 km, takes 2 hours with the wind behind the plane and 2.5 hours return with the flight against the wind. Determine the wind speed and the speed of the plane.
b= SpeedxTime
Step 1) Fill out the distance chart
Step 2) Write 2 eqautions based on the information in the chart and label them 1 and 2
1) 1420= (p+w) 2
2) 1420= (p-w) 2.5
Step 3) Solve the equations
1 420 2p+2w
1420= 2.5p- 2.5w
What is the trick to remembering how to find speed,distance and time?
At the JLC, the Cher concert sold the “good” seats for $100 and the cheaper seats for $65. There are 3 times as many cheap seats at the JLC than good seats. The total receipts were $147 500. Find the number of each type of seat.
Step 1) Write Let Statements
Let x represent the number of good seat
Let y represent the number of cheaper seats
Step 2) Write 2 equations
(1) y=3x
(2) 100x +65y= 147 500
Step 3) Solve the equations using any method
”
Step 4) Write a conclusion
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Two numbers have a difference of 20. Find the numbers if the sum of their squares is a minimum.
Step 1) Write a let Statement
Let x be the first number
Let y be the second number
Step 2) Write 2 equations based on the question, and label 1 and 2
1) y-x=20 → 3) y=20 +x
2) m= x2+ y2
Step 3) Sub 3 into 2
m=x2+ (20+x) 2
m= x2 + (20+x) (20+x)
m= x2+400+20x+20x+x2
m= 2x2 +40x+400
Step 4) Find the Vertex
x= -b/2a
=-40/2(2)
= -40/4
= -10
Step 5) Substitute y=20 +x
y= 20+ (-b)
y= 10
Step 6) Write a conclusion
Therefore the first number is 10 and the second number is -10
A bus company carries about 20 000 riders per day for a fare of 90 cents. A survey indicates that is the fare is decresed, the number of rideres will incrase by 2000 for every 5 cents of decrese. What ticket price would result in the greatest revenue?
Step 1) Write a let statement
Let x represent the number of increment changes
Step 2) Write an equation based on the question
r= Pricex Number of People
= (90-5x) (20 000+ 2 000x)
Step 3) Expand and simplify
r= 1 800 000+ 180 000x- 100 000x - 100 000x2
= -10 000x2+ 80 000x+ 1 800 000
Step 4) Find the vertex
= -80 000/ 2 (-10 000)
= -80 000/ -20 000
= 4 increment changes
Step 4) Find the ticket price
= 90- 5(4)
=90-20
= 70¢
Step 5) Write a conclusion
Therefore the ticket price that would result in the gratest revenue would be 70¢
Mr. Kwok paid $26.00 for movie tickets for himself and 8 children. On another occasion he paid $24.00 for himself and 3 other adults and 4 children. What are the prices for asult and children theatre tickets?
Step 1) Write let statements
Let x be the price of a child ticket
Let y be the price of an adult ticket
Step 2) Write 2 equations based on the given information
(1) y+8x=26
(2) 4y+ 4x=24
A firework is launches into the air. Its height, h in metres, after t seconds is given by the relation h=-4.9 (t-6.3)2 +143
a) What is the maximum height of the firework?
b) When does the firework reach its maximum height?
a) (The constant at the end of the equation)
h=-4.9 (t-6.3)2 +143
Maximum height= 143m
b) (The number in brackets)
h=-4.9 (t-6.3)2 +143
Maxmium height time= 6.3 seconds
