Solving Word Problems Assignment 3

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					                                     MATHEMATICS 10
                           SOLVING SYSTEMS OF LINEAR EQUATIONS
                           SOLVING WORD PROBLEMS ASSIGNMENT 3

 1. Tom is 21 years older than Tim. In 18 years Tom will be twice as old as Tim. How old is each now?

 2. Standard coffee sells for $18.00/kg and premium coffee sells for $24.00/kg. What quantities of each
    should be mixed to create 40 kg of a blend to sell for $22.50/kg?

 3. The sum of two numbers is 56. The larger exceeds twice the smaller by 2. What are the numbers?

 4. Suzanne is twice as old as Mary. Eight years ago the sum of their ages was 41. How old is each now?

 5. Vito invested $500, part at 9% per year and the rest at 11% per year. After one year, the interest earned
   on the 9% investment was $20 less than the interest in the 11% investment. How much did he invest at
   each rate?

 6. A 40% sugar solution is added to an 85% sugar solution to create 1800 ml of a 60% solution. How much
    of the 40% solution is needed?

 7. Rory’s grandmother is 58 years older than Rory. In 5 years, they plan to have a party to celebrate that
    their combined ages have a sum of 100. How old is each now?

 8. An avalanche rescue team travels 8.55 km along a snow covered trail. For the first section, the trail is flat
    and the team averaged a speed of 2.7 km/h. The second section, was mountainous and the team only
    averaged a speed of 1.2 km/h. The one way trip took a total of 4 hours to complete. Determine the
    distance that the team traveled on each section of the trail.

 9. A candy store merchant sells 25 kg of candies for $3.00/kg. If he uses one brand of candies selling for
   $2.25/kg and a second brand of candies selling for $3.75/kg, how much of each brand is required?

10. A boat traveling against the current took 3 hours to travel 36 miles. Traveling with the current, the boat
    took 2 hours for the return trip. Determine the speed of boat in still water.

11. The sum of the digits of a two-digit number is 14. The number formed by reversing the digits is 36 more
    than the original number. What is the original number?

12. Michelle competed in a 16.5 km biathalon comprised of running and swimming. If Michelle ran at a
    speed of 12 km/h and she swam at 3 km/h, how far did she run if she completed the race in 105 minutes?

13. A bank contains $5.20 in dimes and quarters. If the number of quarters is 4 more than twice the number
    of dimes, how many dimes are there?

14. Sterling silver is 92.5% pure silver. How many grams of pure silver and sterling silver need to be mixed
    to obtain 100 grams or a 94% silver alloy?

15. Sue and Rick paddle their canoe 21 km upstream in 7 hours. The return trip downstream takes 3 hours.
    Determine the speed of the canoe and the speed of the current.

 1) Tim = 3 yrs         2) Standard = 10 kg           3) 38 & 18
    Tom = 24 yrs           Premium = 30 kg

 4) Suzanne = 38 yrs    5) $175 @ 9%                  6) 1000 ml of 40% solution
    Mary = 19 yrs          $325 @ 11%

 7) Grandma = 74 yrs    8) Flat Section = 6.75 km    9) 12.5 kg of each brand
    Rory = 16 yrs          Mountain Section = 1.8 km

10) 15 mph             11) Original number is 59    12) Running = 15 km

13) 7 dimes            14) Sterling Silver = 80 g   15) Canoe = 5 km/h
    18 quarters            Pure Silver = 20 g           Current = 2 km/h