If 2 people have 60 shares of stock between them and you double the number of shares of the 1st person and half the number of shares of the 2nd person so that they both have equal shares. How do find the number of shares the 1st person has?
let second person have x shares
then first person has 60-x shares
after doubling-halving .....
second person has x/2
first person has 2(60-x)
then
x/2 = 2(60-x)
x = 4(60-x)
x = 240 - 4x
5x = 240
x = 48
so the first person has 12 shares and the second has 48
check: (1/2)48 = 2(12)
To find the number of shares the 1st person has after doubling their original shares while making both people have an equal number of shares, you can follow these steps:
1. Assign variables to represent the number of shares each person has. Let's take x as the number of shares for the 1st person and y as the number of shares for the 2nd person.
- Initially, we know that x + y = 60 because the total number of shares between them is 60.
2. Apply the given information to create equations. We are told that after doubling the number of shares for the 1st person and halving the number of shares for the 2nd person, they have equal shares.
- The 1st person now has 2x shares.
- The 2nd person now has y/2 shares.
3. Set up an equation to represent the equal shares condition.
- Since they have an equal number of shares, we can say that 2x = y/2.
4. Solve the equations simultaneously. We can use substitution to find the value of x.
- Start by solving the original equation for y.
y = 60 - x
- Substitute y in the equation 2x = y/2:
2x = (60 - x)/2
- Multiply both sides of the equation by 2 to eliminate the fraction:
4x = 60 - x
- Add x to both sides of the equation:
5x = 60
- Divide both sides of the equation by 5 to isolate x:
x = 12
Therefore, the 1st person has 12 shares.