Answer:
The equation is 4x + 3 ....
Let c represents the cost of a candy apple and b represents the cost of a bag of peanuts.
Darius can purchase 3 candy apples and 4 bags of peanuts. So his total cost would be 3c + 4b. Darius can buy 3 candy apples and 4 bags of peanuts in $11.33,so we can write the equation as:
3c + 4b = 11.33 (1)
Darius can purchase 9 candy apples and 5 bags of peanuts. So his total cost would be 9c + 5b. Darius can buy 9 candy apples and 5 bags of peanuts in $23.56,so we can write the equation as:
9c + 5b = 23.56 (2)
<span>Darius decides to purchase 2 candy apples and 3 bags of peanuts. The total cost in this case will be 2c + 3b. To find this first we need to find the cost of each candy apple and bag of peanuts by solving the above two equations.
Multiplying equation 1 by three and subtracting equation 2 from it, we get:
3(3c + 4b) - (9c + 5b) = 3(11.33) - 23.56
9c + 12b - 9c - 5b = 10.43
7b = 10.43
b = $1.49
Using the value of b in equation 1, we get:
3c + 4(1.49) = 11.33
3c = 5.37
c = $ 1.79
Thus, cost of one candy apple is $1.79 and cost of one bag of peanuts is $1.49.
So, 2c + 3b = 2(1.79) + 3(1.49) = $ 8.05
Therefore, Darius can buy 2 candy apples and 3 bags of peanuts in $8.05</span>
Answer:
Step-by-step explanation:
Given:
The equation of the known line is:
A point on the unknown line is (-4, 4)
Now, since the two lines are parallel, their slopes must be equal.
Now, slope of the known line is the coefficient of 'x' which is 
.
Therefore, the slope of the unknown line is also 
Now, for a line with slope 'm' and a point on it 
is given as:
Here, 
. Therefore,
Hence, the equation of the unknown line is .
Answer:
10 hours
Step-by-step explanation:
(150/x) + 1.5 + (450/(x+15)) = 600/x
Multiply through by x(x + 15):
150(x + 15) + 1.5x(x + 15) + 450x = 600(x + 15)
150x + 2250 + 1.5x^2 + 22.5x + 450x = 600x + 9000
150x + 2250 + 1.5x^2 + 22.5x + 450x - 600x - 9000 = 0
1.5x^2 + 22.5x - 6750 = 0
x = (-22.5 +/- sqrt(22.5^2 - 4(1.5)(-6750))) / (2*1.5)
x = (-22.5 +/- sqrt(506.25 + 40500)) / 3
x = (-22.5 +/- sqrt(41006.25)) / 3
x = (-22.5 +/- 202.5) / 3
x = 180/3 or -225/3
x = 60 or -75
But a negative number doesn't make sense, so therefore x = 60, so the journey took 600/60 = 10 hours.
