OAR MAth 2

how many ounces in a pound

16

how many pints in a gallon

8

how many quarts in a gallon

4

how many pounds in a ton

2,000

formula to find degrees in shapes

(# of sides -2)*180= total number of degrees

supplemental angle

adds up to 180

complementary angle

adds up to 90

2r-.5t=5 means …

if 2 times r exceeds one-half of t by 5

3x-1/3*y=9 means…

if 3 times x exceeds 1/3 of y by 9

questions about how fast people can do a job together

time actually needed/time needed to do job alone=1

ex. one recruiter can complete an assignment in 40 minutes; another can complete it in one hour. how long to complete the assignment if they work together? x/40 + x/60=1

x=24 minutes

question with an acid solution. take te pure acid volume of x

P1V1 + P2V2= P3*V3

P1V1 would be X1

P2*V2 is volume of first percentage of first

P3V3= (X+volume of first solution)volume of final

solve for x

ex. how much pure acid must be added to 12 ounces of a 40% acid solution in order to produce a 60% acid solution? 100x+480=60(12+x), x=6

A can complete a project in 20 days and B can complete the same project in 30 days. If A and B start working on the project together and A quits 10 days before the project is completed, in how many days will the project be completed?

A will complete 1/20 of project in 1 day and B will complete 1/30 of project in 1 day. total number of days to complete project is x. B worked for all x days, but A worked for x-10 days. x-10/20 + x-30=1solving for x gives 18 days

discount price questions. amount of discount price =

amount of discount/original =%of reduction

reduction*100=final answer%

traveling/gas mileage/average speed questions

gallons of gas used*miles per gallon =total miles traveled

miles traveled/average speed=hours

a purchaser paid 17.16 for an article that had recently been increased in price by 4%. what was the price before the increase?

x/100=17.16/104

solve for x

16.50

a naval detachment has enough rations to feed 16 people for 10 days. if 4 more people join the detachment , how many fewer days will the rations last?

16*10=160 total rations

4 more people =20 people

160/20 = 8 days

8 is 2 days less

a field can be plowed by 9 machines in 5 hours. if 3 machines are broken and can't be used, how many hours will it take to plow the field?

9*5=45 total hours to complete job

3 broken so 6 will be used

45/6 =7.5 hours

in a 3 hour examination of 320 questions, there are 40 mathematics problems. if twice as much time should be allowed for each math problem as each of the other questions, how many minutes should be spent on math problems?

x=minutes to be spent on each problem

40x+1/2x*280=180

solve for x, x=1 minute

40*1=40 minutes

a tank that holds 450 gallons of water can be filled by 1 pipe in 15 minutes , and emptied by another in 30. how long will it take to fill the tank if both pipes are open

450/15=30 gallons per minute fill

450/30 =15 gallon per minute empty

30gpm-15gpm=15gp

so 450/15gpm=30 minutes

if a driver completes a trip of 120 miles at a rate of 30mph, at what rate would the driver have to travel on the return trip in order to average 40 mph for the round trip?

30mph for 4 hours=120 miles. round trip is 240 miles

240 miles @ 40 mph would take 6 hours

she used 4 hours on the way there, so she has to complete 120 miles in 2 hours

D=R*T, R=60mph

a bridge crosses a river that is 1520 feet wide. one bank of the river holds 1/5 of the bridge and the other holds 1/6. how long is the bridge?

(1/6)x+(1/5)x+1520=x

common denominator: 5x+6x+45600=30x

solve for x=2400 feet long