Answer:
Step-by-step explanation:
Let j represent the cost of a juice box.
Let w represent the cost of a bottle of water.
One teacher purchased 18 juice boxes and 32 bottles of water, and spent $19.92.. This means that
18j + 32w = 19.92 - - - - - - - - - - - - 1
The other teacher purchased 14 juice boxes and 26 bottles of water, and spent $15.76. This means that
14j + 26w = 15.76- - - - - - - - - - - - 2
Multiplying equation 1 by 14 and equation 2 by 18, it becomes
252j + 448w = 278.88
252j + 468w = 283.68
Subtracting, it becomes
- 20j = - 4.8
j = - 4.8/- 20 = 0.24
Substituting j = 0.24 into equation 1, it becomes
18 × 0.24 + 32w = 19.92
4.32 + 32w = 19.92
32w = 19.92 - 4.32 = 15.6
w = 15.6/32 = 0.4875
Kara's prices are incorrect.
the cost of a juice box is $0.24
the cost of a bottle of water is $0.4875
Answer:
12
Step-by-step explanation:
There are many ways to approach this problem. I like a method that uses the least amount of computation. We could figure how much Wendy makes on a bag of chips, the additional amount Wendy wants to make, then divide the latter by the former to find the number of additional bags to sell.
We could use a proportion to figure the number of bags corresponding to $126 in earnings, then subtract the 72 bags already sold. Essentially, we will do this, but without the intermediate numbers.
__
The additional fraction of 72 bags will be ...
(126/108) -1 = 18/108 = 1/6
Then Wendy must sell an additional ...
(1/6)×(72 bags) = 12 bags
to increase her earnings to $126.
Answer:
1029 minutes or 17.15 hours
Step-by-step explanation:
25+0.06M=86.74
0.06M=61.74
M=61.74/0.06=1029
Call the number : x
(1/3)x + 5 = x-6
=> (1/3)x + 5 - (x-6) = 0
=> (1/3)x + 5 - x + 6 = 0
Group (1/3)x with -x, 5 with 6
=> [(1/3)x - x] + (5+6) = 0
=> (-2/3)x + 11 = 0
=> (-2/3)x = -11
=> x = -11 : (-2/3) = 33/2.
Recheck : 1/3 x 33/2 + 5 = 33/6 + 5 = 63/6 = 21/2
33/2 - 21/2 = 12/2 = 6 (21/2 is 6 less than 33/2, satisfied.)
The ladder will reach 122 ft up the building.
The 120 feet of the extended ladder, since it will be leaning against the building, will be the hypotenuse of the right triangle. x will be the height from the top of the fire truck to the point where the ladder hits the building. 75° is the angle the ladder will make with the fire truck.
We have an angle, the side opposite the angle, and the hypotenuse. Opposite/hypotenuse is the ratio for sine, so we set up our equation as such:
x/120 = sin 75
Multiply both sides by 120:
120(x/120) = 120*sin 75
x = 120*sin 75
x ≈116
However, this is just from the top of the fire truck to the point where the ladder hits the building. We still add the 6 feet from the top of the truck to the ground. 116+6 = 122.
