£400 is divided between ann, brian and carol so that ann has twice as much as brian and brian has three times as much as carol. how much does brian receive
a = Ann´s part
b = Brian´s part
c = Carol´s part
Ann has twice as much as Brian means:
a = 2 b
Brian has three times as much as Carol means:
b = 3 c
Put this value in equation:
a = 2 b
a = 2 ∙ 3 c
a = 6 c
Sum of Ann´s part , Brian´s part and Carol´s part is 400.
a + b + c = 400
6 c + 3 c + c = 400
10 c = 400
c = 400 / 10 = 40
Carol´s part = £ 40
b = 3 c
b = 3 ∙ 40 = 120
Brian´s part = £ 120
a = 2 b = 2 ∙ 120 = 240
or which is same
a = 6 c = 6 ∙ 40 = 240
Ann´s part = £ 240
Let's solve this step-by-step:
Let's assign variables to represent the amounts each person receives.
Let A represent Ann's share, B represent Brian's share, and C represent Carol's share.
Given the information:
1. Ann has twice as much as Brian: A = 2B
2. Brian has three times as much as Carol: B = 3C
3. The total amount is £400: A + B + C = £400
Now, let's substitute the second equation into the first equation to relate all three variables:
A = 2B
B = 3C
A = 2(3C)
A = 6C
Substituting the values into the third equation:
A + B + C = £400
6C + 3C + C = £400
10C = £400
C = £400 / 10
C = £40
Now that we know the value of C, let's find the values of A and B:
B = 3C
B = 3 * £40
B = £120
A = 2B
A = 2 * £120
A = £240
Finally, Brian receives £120.
To solve this problem, let's break it down step by step:
Step 1: Assign variables to the unknown amounts
Let’s assign the following variables:
- Let A represent the amount Ann receives.
- Let B represent the amount Brian receives.
- Let C represent the amount Carol receives.
Step 2: Translate the given information into equations
According to the problem:
- Ann has twice as much as Brian, so A = 2B.
- Brian has three times as much as Carol, so B = 3C.
- The total amount divided among them is £400, so A + B + C = 400.
Step 3: Solve the equations
We can use the information from equations (1) and (2) to eliminate variables and only work with one variable. Let's substitute the value of B from equation (2) into equation (1):
A = 2(3C)
A = 6C
Now, we can substitute the value of A from this equation and the value of B from equation (2) into the third equation:
6C + 3C + C = 400
10C = 400
C = 400/10
C = 40
Now we can find the values of A and B:
A = 6C = 6(40) = 240
B = 3C = 3(40) = 120
Step 4: Determine Brian's share
Brian receives £120, according to the values we calculated.
So, Brian receives £120.