Question 56898
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.
.
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.
.
.

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
.
check by plugging in all of the values back into the original equation.