Emily and Sarah had a total of $80 dollars. After Sarah spent 1/3 of her money and emily spent $17, emily had twice as much money as sarah. How much more money did Emily have than sarah at first?
To solve this problem, let's break it down step by step:
Step 1: Set up the equations.
Let's assume the amount of money Sarah had initially as 'x'. Therefore, the amount of money Emily had initially would be (80 - x).
Step 2: Determine Sarah's money after spending 1/3.
Sarah spent 1/3 of her money, which is (1/3) * x = x/3. So, after spending, Sarah would have x - (x/3) = 2x/3.
Step 3: Determine Emily's money after spending $17.
Emily's initial money was (80 - x). After spending $17, she would be left with (80 - x - 17) = (63 - x).
Step 4: Formulate an equation based on the given condition.
According to the problem, we know that after spending, Emily had twice as much money as Sarah. Therefore, we can set up the equation:
63 - x = 2(2x/3).
Step 5: Solve the equation.
Let's simplify the equation and solve for x:
63 - x = 4x/3
3(63 - x) = 4x
189 - 3x = 4x
189 = 7x
x = 189/7
x ≈ 27
Step 6: Calculate the difference between their initial amounts.
Now that we have found the initial amount of money Sarah had, we can calculate the difference between Emily and Sarah's initial amounts:
Difference = (80 - x) - x
Difference = 80 - 2x
Difference = 80 - 2(27)
Difference = 80 - 54
Difference = 26
Therefore, Emily had $26 more than Sarah initially.
e+s = 80
e-17 = 2(2/3 s)
Now just solve for e and s, and then get e-s.