Question 56898: 2. Board Cutting. A 72 inch board is cut into two pieces. one piece is 2 inches longer than the other. find the length of the piece?
7. Iditarod Race. The Iditarod dog sled race extends for 1049 mi from Ancorage to Nome. If a musher is twice as far from Ancorage as from Nome, how much of the race has the musher completed?
22. Van Rental. Value Rent-A-Car rents vans at a daily rate of $84.95 plus 60 cents per mile. Molly rents a van to deliver electrical parts to her customers. She is alloted a daily budget of $320. How many miles can she drive for $320?
31. Taxi fares. In Benifold, taxis charge $3 plus 75 cents per mile for an airport pickup. How far from the airport can courtney travel for $12?
Answer by tutorcecilia(2152)   (Show Source):
You can put this solution on YOUR website! 2. Since the board was cut into two parts:
Piece #1 + Piece#2=72
x+x=72
Since one piece is 2 inches longer than the other, than:
x+(x+2)=72 [Combine like-terms and solve for x]
2x+2=72
2x=72-2
2x=70
x=70/2
x=35 (Part #1)
Piece # 2= (x+2)=35+2=37
35+37=72 [Plug the value for (x=35) back into the original equation.
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7. Distance #1 + Distance #2=1049
x+x=1049
2x+x=1049 [Because, a musher is twice as far from Ancorage as from Nome]
3x=1049
x=349.666 (Distance left to Nome]
(2)(349.66)=699.333 miles away from Anchorage (distance completed)
.
Check by adding the distances together.
22. Use the slope-intercept formula since there is a linear relationship between the number of miles traveled and the amount of rental per miles:
y=mx+b
y=.60x+84.95 [Because the flat rental is $84.95 plus .60cents for every unknown mile (x)]
$320=.60x+84.95 [Because the total rental cannot exceed $320.]
320=.60x+84.95 [Simplify and solve for x (the unknown milage]
320-84.95=.60x
235.10=.60x
235.10/.60=x
391.83=x (the unknown mileage driven]
Check by plugging all of the variables back into the original equation.
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31. This is also a linear equation because as the miles increase so does the fare.
y=mx+b
y=.75x+$3 [Because, the flat fee is $3.00 and .75 cents is charged for each (x)unknown mile thereafter.]
$12=.75x+3 [Solve for x]
12=.75x+3
12-3=.75x
9=.75x
x=9/.75
x=12 miles can be traveled for $12
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check by plugging in all of the values back into the original equation.
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