Abel ,Belle and Cindy have $408 altogether. Belle has $7 more than Cindy And $5 more than Abel. how much does Abel have?
A + B + C = 408
B = C + 7 = A + 5 ... A = B - 5 ... C = B - 7
solve by substitution
Cindy has $X.
Belle has $(X+7).
Abel has $(X+7)-5.
x + (x+7) + (x+7)-5 = 408.
3x = 399,
X = 133.
Abel amt. = (x+7)-5 = (133 + 7)- 5 = $135.
Thank you for your quick response. It is very clear.
Charlie
Glad I could help.
To solve this problem, we can set up a system of equations to represent the given information. Let's assign variables to represent the amount of money each person has:
Let A represent the amount Abel has.
Let B represent the amount Belle has.
Let C represent the amount Cindy has.
We know that Abel, Belle, and Cindy have a total of $408 altogether, so our first equation is:
A + B + C = 408
We also know that Belle has $7 more than Cindy and $5 more than Abel. This can be expressed in the following equations:
B = C + 7
B = A + 5
Now we can solve the system of equations to find the value of A, which represents the amount Abel has.
We'll start by substituting the second equation into the third equation:
C + 7 = A + 5
Next, we'll substitute the values of B and C from the second equation into the first equation:
A + (C + 7) + C = 408
A + 2C + 7 = 408
A + 2C = 408 - 7
A + 2C = 401
Now we have a system of two equations:
A + 2C = 401
C + 7 = A + 5
We can solve this system by substitution or elimination.
Let's use substitution and solve for A:
C + 7 = A + 5
A = C + 7 - 5
A = C + 2
Substitute this expression for A in the first equation:
(C + 2) + 2C = 401
3C + 2 = 401
3C = 401 - 2
3C = 399
C = 399 / 3
C = 133
Now we know that Cindy has $133.
To find how much money Abel has, substitute the value of C into the expression for A:
A = C + 2
A = 133 + 2
A = 135
Therefore, Abel has $135.