$420 is divided between A & B so that A gets 3/7 th of what B gets.what amount doea A get?
represent this: let a be 3/7b and let b be b,since they share the money: b+3/7b=420,then find b,and a(a=3/7b)
According to the method A=126..but the ans is given A=180..but how?
Divide the $420 into 10 parts of $42 each.
A gets 3 parts, or $126
B gets 7 parts, or $294
In order for A to get 180, either
B gets 420 or a gets 3/7 of the total, not 3/7 of B's share.
To find the amount A gets, we need to follow these steps:
Step 1: Assign variables to the unknowns.
Let's say the amount that B gets is x.
Step 2: Set up the equations.
We know that A gets 3/7 of what B gets. So, A = (3/7) * x.
Also, we know that the sum of A and B's amounts is $420. Therefore, A + B = $420.
Step 3: Solve the equations.
Substitute the value of A from the first equation into the second equation:
(3/7) * x + B = $420.
Now, we need to solve for B.
Subtract (3/7) x from both sides:
B = $420 - (3/7) x.
Step 4: Find the value of B.
We can substitute the value of B from the equation above into the second equation:
(3/7) * x = $420 - (3/7) x.
To simplify, we can multiply both sides of the equation by 7 to get rid of the fraction:
3x = 7($420) - 3x.
Combine the x terms:
3x + 3x = 7($420).
Simplify further:
6x = 7($420).
Divide both sides of the equation by 6:
x = (7($420))/6.
Step 5: Calculate the value of A.
Now that we know the value of x, we can substitute it back into the first equation to find A:
A = (3/7) * x.
Substitute x with its value:
A = (3/7) * ((7($420))/6).
Simplify further:
A = (($420 * 7)/6) * (3/7).
Cancel out the common factors:
A = ($420 * 1) * (1/2).
Multiply the remaining fractions:
A = ($420/2).
Finally, simplify:
A = $210.
Therefore, A gets $210.