The ratio of the volume of water in Jug A to the volume of water in Jug B is 2:5.
A.) If half of the water in Jug A is poured into Jug B, what is the new ratio of the volumes of water in Jug A to Jug B?
B.) If half of the water in Jug B is poured into Jug A, what is the new ratio of the volumes of water in Jug A to Jug B?
C.) If 1/3 of the water in Jug A is poured into Jug B, what is the new ratio of the volumes of water in Jug A to Jug B?
original in A is 2x
and in B is 5x
A) half of A into B
jug A now has 2x - x = x
jug B now has 5x + x = 6x
new ratio is x : 6x = 1 : 6
B) half of B into A
B has 5x - 5x/2 = 5x/2
A now has 5x + 5x/2 = 5x/2
New ration = 5x/2 : 5x/2 = 1 : 1
Follow my method to do C)
a. 1:6
b. 9:5 (4.5:2.5 )
c. 4:17
2:3
Thanks for helping me
I didn’t see number c
A.) If half of the water in Jug A is poured into Jug B, we are essentially pouring 1 part of water from Jug A to Jug B. Since the ratio of the volumes of water in Jug A to Jug B is 2:5, let's consider 2 parts for Jug A and 5 parts for Jug B. After pouring 1 part from Jug A to Jug B, Jug A will have 2 parts - 1 part = 1 part. Jug B will have 5 parts + 1 part = 6 parts. So, the new ratio of water in Jug A to Jug B is 1:6.
B.) If half of the water in Jug B is poured into Jug A, we are pouring 1 part of water from Jug B to Jug A. Since the initial ratio of the volumes of water in Jug A to Jug B is 2:5, let's consider 2 parts for Jug A and 5 parts for Jug B. After pouring 1 part from Jug B to Jug A, Jug A will have 2 parts + 1 part = 3 parts. Jug B will have 5 parts - 1 part = 4 parts. So, the new ratio of water in Jug A to Jug B is 3:4.
C.) If 1/3 of the water in Jug A is poured into Jug B, we are pouring 1 part out of 3 parts. Considering the initial ratio of the volumes of water in Jug A to Jug B as 2:5, let's consider 2 parts for Jug A and 5 parts for Jug B. After pouring 1/3 part from Jug A to Jug B, Jug A will have 2 parts - (1/3) part = 5/3 parts. Jug B will have 5 parts + (1/3) part = 16/3 parts. Simplifying, the new ratio of water in Jug A to Jug B is (5/3):(16/3), which can further be simplified to 5:16.
To solve these questions, we need to understand the concept of ratio and how it changes when we perform certain operations.
A.) If half of the water in Jug A is poured into Jug B:
To find the new ratio, we first need to calculate how much water is transferred from Jug A to Jug B. Since the ratio of the volumes of water in Jug A to Jug B is 2:5, we can represent this as 2x:5x (where x represents a common factor).
If half of the water in Jug A is poured into Jug B, we can divide the original volume of Jug A by 2:
Volume of water in Jug A after pouring half = 2x / 2 = x
Now, we need to calculate the new volume of water in Jug B. Since the transferred water is x, and the original volume of water in Jug B is 5x, we subtract x from 5x to get:
Volume of water in Jug B after pouring = 5x - x = 4x
Therefore, the new ratio of the volumes of water in Jug A to Jug B is x : 4x.
B.) If half of the water in Jug B is poured into Jug A:
Using the same initial ratio of 2:5, we can represent the volumes of water in Jug A and Jug B as 2x and 5x respectively.
If half of the water in Jug B is poured into Jug A, we need to calculate the amount transferred from Jug B to Jug A.
The transferred water volume will be half of the original volume of Jug B, which is (1/2) * 5x = (5/2)x.
Now, we need to calculate the new volumes of water in Jug A and Jug B:
New volume of water in Jug A = 2x + (5/2)x = (9/2)x
New volume of water in Jug B = 5x - (5/2)x = (5/2)x
Thus, the new ratio of the volumes of water in Jug A to Jug B is (9/2)x : (5/2)x. This ratio can also be simplified to 9:5.
C.) If 1/3 of the water in Jug A is poured into Jug B:
Similarly, we start with the initial ratio of 2:5 for the volumes of water in Jug A and Jug B.
To determine the amount transferred from Jug A to Jug B, we calculate one-third of the volume of Jug A:
Transferred volume = (1/3) * 2x = (2/3)x
The new volumes of water in Jug A and Jug B can be calculated as follows:
New volume of water in Jug A = 2x - (2/3)x = (4/3)x
New volume of water in Jug B = 5x + (2/3)x = (17/3)x
Therefore, the new ratio of the volumes of water in Jug A to Jug B is (4/3)x : (17/3)x. This ratio can also be simplified to 4:17.