Answer:
System of equations:
20x + 30y = 650
x + y = 25
Time underwater = 10 hours
Time at the surface = 15 hours
Step-by-step explanation:
Let x = time underwater at 20 km/h.
Let y = time on the surface at 30 km/h.
speed = distance/time
distance = speed * time
distance underwater: 20x
distance on the surface: 30y
total distance: 650
20x + 30y = 650
total time: x + y
total time: 25
x + y = 25
20x + 30y = 650
x + y = 25
20x + 30y = 650
-20x - 20y = -500
--------------------------------
10y = 150
y = 15
x + y = 25
x + 15 = 25
x = 10
Answer:
54
Step-by-step explanation:
The ratio of 6 to 4 between the length and the with means that if the length was 6, the width would be 4.
We can represent this in a table:
Length Width
6 ⇒ 4
and we need to find the length for a picture frame that has a width of 36. If we represent the length of the picture frame by x, and we update the previous table:
Length Width
6 ⇒ 4
x ⇒ 36
The value of x (the length) can be found by the rule of three: Multiply the cross quantities in the last table ( 6 by 36) and divide the result by the remaining value (4).
We get the following for x:
x = 6*36/4
x= 216 / 4
x = 54
The length is 54.
Another way to find the result is:
The width of the frame (36) is 9 times more than the width that the ratio indicates (4). Because
4*9 = 36
thus, the same must be true for the relationship between the length in the indicated ratio and the length of the frame (9 times bigger):
6*9 = 54
we also get 54 as the result.
9514 1404 393
Answer:
36
Step-by-step explanation:
Let n represent the number of stickers Ms Galinia has. Then the number of students is ...
(n -12)/3 . . . for first distribution of stickers*
(n +4)/5 . . . for the second distribution of stickers
Since the number of students has not changed, we can equate these values:
(n -12)/3 = (n +4)/5
5(n -12) = 3(n +4)
5n -60 = 3n +12
2n = 72
n = 36
Ms Galinia has 36 stickers.
_____
* If Ms Galinia has 12 left over after giving 3 to each student, then subtracting 12 from her number of stickers will give a number that is 3 times the number of students. Dividing (n-12) by 3 will give the number of students. Similar reasoning can be used for the 5-per student distribution.
One could write equations using a variable for the number of students, or variables for both students and stickers. Since we only need to know the number of stickers, it seemed reasonable to use one variable for that.
The answer would be d. Hope it helps! If anyone else answers, can you vote my answer to be the brainiest? Thanks!