10% of Ivan's savings was $18 more than 30% of Ben's savings. After Ivan spent 7/10 of his savings and Ben spent 40% of his savings, Ivan had $93 more than Ben. How much was Ivan's saving at first?
0.10i = 18 + 0.30b
3/10 i = 93 + 0.60b
now just solve for i
Let's assume Ivan's savings to be x.
According to the given information, 10% of Ivan's savings was $18 more than 30% of Ben's savings.
So, we can write the equation: 0.10x = 0.30 * Ben's savings + $18
Next, after Ivan spent 7/10 of his savings and Ben spent 40% of his savings, Ivan had $93 more than Ben.
Let's calculate the remaining savings of Ivan after spending 7/10 of his savings:
Remaining savings of Ivan = (1 - 7/10) * x = 3/10 * x
Let's calculate the remaining savings of Ben after spending 40% of his savings:
Remaining savings of Ben = (1 - 40%) * Ben's savings = 60% * Ben's savings = 0.60 * Ben's savings
According to the last given information, Ivan had $93 more than Ben, so we can write the equation: 3/10 * x - 0.60 * Ben's savings = $93
Now we have two equations:
1. 0.10x = 0.30 * Ben's savings + $18
2. 3/10 * x - 0.60 * Ben's savings = $93
We can solve these two equations simultaneously to find the value of x, which represents Ivan's savings at first.
To solve this problem, let's break it down step by step:
1. Let's assume Ivan's initial savings as "x".
2. According to the problem, 10% of Ivan's savings was $18 more than 30% of Ben's savings. This can be written as:
0.1x = 0.3B + 18 -- Equation 1
where B represents Ben's savings.
3. Next, the problem states that after Ivan spent 7/10 of his savings and Ben spent 40% of his savings, Ivan had $93 more than Ben. We can set up another equation using this information:
(x - 0.7x) = (B - 0.4B) + 93 -- Left side represents Ivan's remaining savings, and the right side represents Ben's remaining savings.
Simplifying this equation, we get:
0.3x = 0.6B + 93 -- Equation 2
Now, we have a system of two equations (Equation 1 and Equation 2) that we can solve simultaneously.
To solve the system of equations, we can use substitution or elimination method. Let's use the substitution method:
Step 1: Solve Equation 1 for B:
0.1x = 0.3B + 18
0.3B = 0.1x - 18
B = (0.1x - 18) / 0.3
B = (x - 180) / 3 -- Equation 3
Step 2: Substitute Equation 3 into Equation 2:
0.3x = 0.6((x - 180) / 3) + 93
0.3x = 0.2x - 120 + 93
0.3x - 0.2x = -27
0.1x = -27
x = -27 / 0.1
x = -270
Now, we have found that Ivan's initial savings were -270 dollars. However, negative savings does not make sense in this context. Please double-check the information given in the problem or ensure the calculations are correctly entered.