If A gives B $3, B will have twice as much as A. If B gives A $5, A will have twice as much as B. How much does each have? Explain clearly your working.
A now has x
B now has y
The wording is confusing.
Are the consecutive transfers of money, or are they independent events
Case1 : consecutive events
A gives $3 to b
A now has A-3, B has y+3
y+3 = 2(x-3)
y+3 = 2x - 6
2x - y = 9 , #1
B gives $5 to A
A now has x-3 + 5 = x+2
B now has y+3 - 5 = y - 2
x+2 = 2(y-2)
x+2 = 2y - 4
x - 2y = -6 , #2
#1 times 2
---> 4x-2y=18
#2 --> x - 2y = -6
subract:
3x = 24
x = 8
then y = 7
A has $8 and B has $7
first transfer, A give $3 to B
A has 5 , and B has 10 , Does B have twice A ? yup
2nd transfer , B gives $5 to A
A has 10 , B has 5, does A have twice of B ? , yup
Case 2: independent events:
A gives $3 to B
y+3 = 2(x-3)
y = 2x - 9
B gives $5 to A
A has x+5, B has y-5
x+5 = 2(y-5)
x = 2y - 10 - 5
x = 2(2x-9) - 15
x = 4x - 33
-3x = -33
x = 11
y = 13
This too can be verified.
Pick your interpretation.
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Let's assume A's initial amount of money is 'x' dollars and B's initial amount of money is 'y' dollars.
According to the given information, if A gives B $3, B will have twice as much as A. This can be expressed as:
B's amount of money = 2 * A's amount of money
y + 3 = 2x
Similarly, if B gives A $5, A will have twice as much as B. This can be expressed as:
A's amount of money = 2 * B's amount of money
x + 5 = 2(y - 5)
We now have a system of two equations with two variables:
Equation 1: y + 3 = 2x
Equation 2: x + 5 = 2(y - 5)
To solve these equations, we can use substitution or elimination method. Let's use substitution method to solve this system of equations:
Step 1: Rearrange Equation 1 to solve for y in terms of x:
y = 2x - 3
Step 2: Substitute the value of y in Equation 2:
x + 5 = 2((2x - 3) - 5)
Step 3: Simplify and solve for x:
x + 5 = 2(2x - 8)
x + 5 = 4x - 16
3x = 21
x = 7
Step 4: Substitute the value of x in Equation 1 to find y:
y + 3 = 2(7)
y + 3 = 14
y = 11
Therefore, A has $7, and B has $11.