Mr. Vogt’s “Word Problems Part 2”

 

1.  A collection of coins consisting of nickels, dimes, and quarters is worth $4.55.  There are twice as many nickels as dimes and seven more dimes than quarters.  How many of each denomination will be found in the collection?

2.  A box contains shotput balls of two types:  8 lb. and 15 lb.  There are 16 balls weighing 170 lb.  How many of each type are there?

3.  How many gallons of water must be added to 70 gal. of a 30% chlorine solution in order to produce a 20% chlorine solution?

4.  How many gallons of chlorine must be added to 70 gal. of a 20% chlorine solution in order to produce a 30% chlorine solution?

5.  A chemist needs a 55% acid solution which he will create by mixing a 45% acid solution with a 70% acid solution.  If he needs 20 liters of solution, how much of each must he use?

6.  At noon a private plane left Austin, Texas for Los Angeles, California, 2100 kilometers away, flying at 500 km/h.  One hour later a jet left L.A. for Austin at 700 km/h.  At what time did they pass each other?

7.  At 8 am we left the camp and drove the park’s speed limit.  Our friends, who always drive 12 mph faster than the posted speed limit, left the same site at 8:20 am and caught up to us at 9:40 am.  How fast were they driving?

8.  Joe hiked up a mountain trail to the top of the hill at 4 mph and back down at 6 mph.  It took him 5 hours to make the round trip.  How far is it from the beginning of the trail to the top of the hill?

9.  A ship must average 22 knots (nautical miles per hour) to make its 10-hour run on schedule.  During the first four hours bad weather caused it to reduce its speed to 16 knots.  What should its average speed be for the rest of the trip in order to be on schedule?

10.  Your rectangular backyard is 20’ x 30’.  You are having a pool installed and tell the contractor that you want to center it in the yard with a uniform walkway all the way around it.  He quotes you a price for a pool that will take 416 ft² of the yard.  What are the dimensions of the pool and how wide is the walkway to be?  Also, if you are installing non-slip tiles that are 1’ x 1’ (1 sq. ft.) all the way around the pool, how many tiles will you need?

11.  In question #10, what if the yard is 26’ x 22’ and the pool is 320 ft² ?  Give answer for the pool, walkway, and tiles.

12.  A man flew his plane against a stiff wind and it took him 7 hours to make his 875 mile trip.  Flying back with the same wind (wind at the same speed) pushing him along the trip only took 5 hours.  If he was going full speed both times, how fast can his plane go in still air and how fast was the wind?

13.  Patrick and Patricia started from the same place and went in opposite directions with Pat traveling 10 mph faster than Patty.  If they drove 660 miles in 6 hours then how fast was Patrick driving?  How fast was Patricia moving?

14.  A massage parlor offers a year’s membership for $150 and then only charges $10 per hour.  Their non-membership price is $35 per hour.  Find the break (even) point and explain what your answer means.  Is the membership a good deal (in your opinion)?

15.  A man invested $300 into each of two accounts (for a total of $600).  The second account had 4 times the annual interest rate of the first.  If he earned $225 in combined interest for the year, what were the two interest rates?

16.  If you take three consecutive integers and increase each by four and then find their average it is equal to the sum of the three integers.  Find the integers.

17.  Club 1 charges $6 for entrance and $1 a drink (soda), Club 2 has no entrance fee, but charges $3 a drink.  Find the break point and explain which is the better club to patronize.

18.  A box of calculators cost $48.  If the price of each calculator is lowered by $2 then you could afford to buy 2 more of them.  How many calculators in a box and how much does each one cost?

 

Answers:

1.) 28 n, 14 d, 7 q         2.) 10 eight lb, 6 fifteen lb          3.) 35 gal               4.) 10 gal           5.) 12 L of 45%, 8 L of 70%

6.) 2:20 pm               7.) 60 mph          8.) 12 mi              9.) 26 knots         10.) 16’ x 26’ with a 2’ walkway, 88 tiles

11.) 20’ x 16’ with a 3’ walkway, 324 tiles             12.) Speed = 150 mph, Current = 25 mph            13.) 85 mph, 75 mph

14.) 6 hours (if you want to visit more than 6 times (at an hour per visit) it is cheaper to pay the membership)   15.) 15% and 60%

16.) (1,2,3)            17.) 3 drinks (if you plan on having more than three drinks it is cheaper to pay the entrance fee.)      18)  6, $8.00

 

* Vogt Educational Materials