A bus travels two different routes: the Green Route and the Blue Route. The routes are different lengths.
On Monday the bus traveled the Green Route 6 times and the Blue Route 5 times, traveling a total of 52 miles. On Tuesday the bus traveled the Green Route 12 times and the Blue Route 13 times, traveling a total of 119 miles.
What is the length of the Green Route in miles?
A. 4.4 mi
B. 4.5 mi
C. 6.4 mi
D. 6.8 mi
C. 6.4 mi
Let's denote the length of the Green Route as G and the length of the Blue Route as B.
From the given information, we can set up the following system of equations:
6G + 5B = 52
12G + 13B = 119
Now, we can solve these equations simultaneously to find the length of the Green Route:
Multiplying the first equation by 13 and the second equation by 5 to eliminate B, we get:
78G + 65B = 676
60G + 65B = 595
Subtracting the second equation from the first, we have:
18G = 81
G = 81/18
G = 4.5
Therefore, the length of the Green Route is 4.5 miles.
A manager purchased a total of 21 coffee mugs and key chains. Each coffee mug cost $8.50, and each key chain cost $2.75. If the manager spent a total of $132.50, how many coffee mugs did the manager purchase?
Let's denote the number of coffee mugs purchased as 'C' and the number of keychains purchased as 'K'.
From the given information, we can set up the following system of equations:
C + K = 21 (equation 1)
8.50C + 2.75K = 132.50 (equation 2)
Now we can solve this system of equations to find the number of coffee mugs purchased:
From equation 1, we can rewrite it as C = 21 - K and then substitute this into equation 2:
8.50(21 - K) + 2.75K = 132.50
178.5 - 8.50K + 2.75K = 132.50
178.5 - 5.75K = 132.50
-5.75K = -46
K = 46 / 5.75
K = 8
Substitute K = 8 back into C = 21 - K:
C = 21 - 8
C = 13
Therefore, the manager purchased 13 coffee mugs.