Solving Word Problems With Equations Of One Degree And One Unknown Worksheet With Answers Page 7
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20After the chart is completed, we return to the problem for the relationship that
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gives us our equation.
It reads “total yearly interest is $1040.” So, our equation is
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0.04X + 0.06(24000 - X) = 1040
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Solving: Multiply each term by 100 to remove decimals.
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4x + 6(24000 – x) = 104000
4x + 144000 - 6x = 104000
14400 - 2X = 104000
-2X = -40000
X = 20000
We were asked to find the amount invested at 4%. Since we represented that
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amount by “x”, we conclude: the amount invested at 4% is $20,000 and the
amount invested at 6% is $4000
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DISTANCE PROBLEMS
Many students find these hardest of all, but if you follow the steps you can master them.
ADDITIONAL HINTS (FOR DISTANCE PROBLEMS)
Traveling with the current (down stream) or wind increases the speed of the
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vehicle by the speed of the current or wind. (E.g. If you travel 40 mph in still air
and there is 30 mph wind, moving with the wind means you actually travel 70
mph.)
Traveling against the current (upstream) or wind decreases the speed of the
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vehicle by the speed of the current or the wind. (E.g. In the previous example,
moving against the wind means you actually travel 10 mph.)
The basis of all distance problems is the formula: D = r * t (Distance = rate X
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time);
Rate is the same as speed.
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EXAMPLE
1. At a given time a man on a bicycle is 10 miles ahead of a car. Both are traveling in
the same direction. The bike is traveling at 15 mph and the car at 35 mph. How many
hours has each traveled when they meet?
Read the above very carefully.
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You are dealing with a DISTANCE (MOTION) PROBLEM.
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It is best to make a diagram as well as a chart for these problems
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The chart for a distance problem looks like this
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Rate
Time
Distance
First Vehicle
Second Vehicle
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