WEIGHTED AVERAGES
LIT. EQUATIONS+DIM. ANALYSIS
MULTI-STEP EQUATIONS
RATE OF CHANGE AND SLOPE
RATIOS AND PROPORTIONS
100
A person biking travels 15 mi. in 1 hour. The same person biking down hill travels 15 miles in 0.5 hrs. Find the average speed of the person.
What is 20 mph
100
Solve 2x + 8y = 48 for y.
What is y=-1/4x+6
100
Find two consecutive integers whose sum is -13.
What is -6, -7
100
Find the slope of the line that passes through (5, -5) and (9, -5).
What is 0
100
In Mrs.Jasper's class, the ratio of passing grades to failing grades is 7 to 5. How many of the 36 students failed the quiz?
What is 15 students failed
200
Jo has 50 milliliters of a 10% acid solution. How many milliliters of 45% acid solutions should he add to create a 35% solution?
What is 125 milliliters
200
Use the formula A = lw to find the width of a rectangle whose area is 46.875 square meters and whose length is 7.5 meters.
What is 6.25 meters
200
Solve 0.2x + 0.9 = 0.3 – 0.1x
What is x = –2
200
Every hour, your sister can make the same number of socks. If in the 3rd hour of work, she has made 6 pairs of socks, and by the 5th hour, she has made 10 pairs of socks, what is the rate at which she made the socks?
What is m = 2
200
In the park mentioned above, the ratio of ducks to geese is 16 to 9. How many of the 300 birds are geese?
What is 108 geese
300
Fruit costs $1.95/lb, and candy costs $1.25/lb. How many lbs. of fruit should be added to 4 lbs. candy to make a mix of $1.45/lb?
What is 2 lbs.
300
Solve P = 2l + 2w for w
What is (p-2l)/2=w
300
Solve 11 + 3x– 7 = 6x + 5 – 3x
What is no solution
300
find the slope of y = ( 3/5 )x – 2
What is m = 3/5
300
Consider those ducks and geese we counted back at the park. Their ratio was 16 ducks to 9 geese. Suppose that there are 192 ducks. How many geese are there?
What is 108 geese
400
Dee drove 60 miles.The trip took 1 hr. 15 min. On the way back the trip took 1 hr. 30 min. Find the average speed for the round trip.
What is 44 miles per hour
400
Solve Q = 3a + 5ac for a
What is Q/(3+5c)=a
400
13 – (2x + 2) = 2(x + 2) + 3x
What is x=1
400
The equation for the speed (not the height) of a ball that is thrown straight up in the air is given by v = 128 – 32t, where v is the velocity (in feet per second) and t is the number of seconds after the ball is thrown. With what initial velocity was the ball thrown? What is the meaning of the slope?
What is every second, the speed decreases by 32 feet per second. Eventually the velocity becomes zero (when the ball reaches its peak), and then becomes negative (when gravity takes over and pulls the ball back down to the ground).
400
2 : x = 3 : 9
What is x=6
500
An executive drove from home at an average speed of 30 mph to an airport where a helicopter was waiting. The executive boarded the helicopter and flew to the corporate offices at an average speed of 60 mph. The entire distance was 150 miles; the entire trip took three hours. Find the distance from the airport to the corporate offices.
What is 120 miles
500
Solve A = ( 1/2 )ah – ( 1/2)bh for h
What is 2A/(a-b)=h
500
11.5(12.6n + 8.2) + 5.3 = 0.4(n + 7.6) − 11n
What is -0.62
500
Fisherman in the Finger Lakes Region have been recording the dead fish they encounter while fishing in the region. The Department of Environmental Conservation monitors the pollution index for the Finger Lakes Region. The model for the number of fish deaths "y" for a given pollution index "x" is y = 9.607x + 111.958. What is the meaning of the slope? What is the meaning of the y-intercept?
What is for every increase in the pollution index by one unit (say, from a pollution index of 6 to a pollution index of 7), there are nine or ten more fish deaths during the year.
500
Find the unknown value in the proportion: (2x + 1) : 2 = (x + 2) : 5
What is x = –1/8
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