The ratio of Julie to Joseph's savings was 4 : 7 at first. After Julie saved another $180 and Joseph saved another $60, Julie had twice of Joseph. How much did Julie have in the end?
Question
The ratio of Julie to Joseph's savings was 4 : 7 at first. After Julie saved another 60, Julie had twice of Joseph. How much did Julie have in the end?
Solution
Let's solve this step by step:
Step 1: Let's assume the initial savings of Julie and Joseph are 4x and 7x respectively.
Step 2: According to the problem, Julie saved another 60. So, their savings become (4x + 180) and (7x + 60) respectively.
Step 3: It is given that after saving additional money, Julie had twice of what Joseph had. So, we can set up the equation as follows: 4x + 180 = 2 * (7x + 60)
Step 4: Simplify the equation: 4x + 180 = 14x + 120
Step 5: Rearrange the equation to find the value of x: 14x - 4x = 180 - 120, which simplifies to 10x = 60
Step 6: Solve for x: x = 60 / 10 = 6
Step 7: Substitute x = 6 into the equation for Julie's savings: 4x + 180 = 4*6 + 180 = 24 + 180 = $204
So, Julie had $204 in the end.
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