Solving Applied Problems: Two Equations?

Solve.

1.) Radio Airplay. Rudy must play 12 commercials during his 1-hr radio show. Each commercial is either 30 seconds or 60 seconds long. If the total commercial time during the hour is 10 minutes, how many commercials of each type does Rudy play?

2.) Etch Clean Graphics uses one cleanser that is 25% acid and a second that is 50% acid. How many liters of each should be mixed to get 10 L of a solution that is 40% acid?

3.) Darren paddled for 4 hr with a 6-km/h current to reach a campsite. The return trip against the same current took 10 hr. Find the speed of Darren's canoe in still water.

1 Answer

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  • 7 years ago
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    Let the no of " 60 seconds " commercial be x

    Then the no of "30 seconds " commercial will be 12 - x

    Total commercial time = 60x + 30 (12-x) = 10*60

    60x +360 - 30x = 600

    30x = 240

    x = 8

    ANSWER 8 commercials ( 60 seconds) AND 4 commercials ( 30 seconds)

    CHECK

    8X 60 = 480

    4X 30 = 120

    ADD = 600 seconds = 10 minutes

    2) Let the quantity of 50% acid mixed be x liters

    Then the quantity of 25% acid mixed will be (10 - x) liters

    0.50x + 0.25 ( 10-x) = 0.40*10

    0.50x + 2.50 - 0.25x = 4

    0.25x = 1.50

    x = 6

    ANSWER 6 liters (50%) and 4 liters (25%)

    CHECK

    0.50 X 6 = 3

    0.25 X 4 = 1

    ADD 4

    4/10 X 100 = 40%

    3) Let the speed of Darren's canoe in still water be x km/ hour

    Speed of current = 6km/ hour

    DOWNSTREAM

    -------------------------

    Speed = ( x+6) km/ hour

    Distance traveled = Speed X time

    = ( x+6) X 4 = 4x +24 km

    UPSTREAM

    ----------------

    Speed = ( x-6) km/ hour

    Distance = 10 ( x-6) = 10x -60 km

    DISTANCE TRAVELED EACH WAY IS SAME

    10x - 60 = 4x + 24

    6x = 84

    x = 14

    ANSWER 14km/ hour

    CHECK

    4 ( 14+6) = 80km

    10 ( 14-6) = 80km

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