Amy, Betty and Clara went shopping together. Amy spent 20% more than Betty. Betty spent 25% more than Clara. If Amy spent $58 more than Clara, how much did they spend altogether?
(Please Show Working Clearly and try not to use Algebra)
a = 1.2b
b = 1.25c
a = c+58
Time to stop avoiding algebra!
1.2(1.25c) = c+58
1.5c = c+58
0.5c = 58
c = 116
Clara spent 116
Amy spent 174
Betty spent 174/1.2 = 145
so, add them all up.
To solve this problem without using algebra, we can break it down step by step.
Let's start by assuming that Clara spent a certain amount. Since Betty spent 25% more than Clara, we can calculate Betty's spending as 125% of Clara's spending.
Next, we know that Amy spent 20% more than Betty. So, Amy's spending can be calculated as 120% of Betty's spending.
Given that Amy spent $58 more than Clara, we can set up the following equation:
Amy's spending - Clara's spending = $58
120% of Betty's spending - Clara's spending = $58
Now, let's use this equation to solve the problem step by step:
1. Start with Clara's spending as x (the unknown amount).
2. Betty's spending is 125% of Clara's spending, which can be calculated as 1.25x.
3. Amy's spending is 120% of Betty's spending, which can be calculated as 1.2 * (1.25x).
4. Set up the equation: 1.2 * (1.25x) - x = $58.
Simplify: (1.5x) - x = $58.
5. Combine like terms: 0.5x = $58.
6. Divide both sides by 0.5: x = $116.
7. Clara spent $116, Betty spent 125% of $116, which is $145, and Amy spent 120% of $145, which is $174.
8. To find the total amount spent altogether, add Clara's, Betty's, and Amy's spending: $116 + $145 + $174 = $435.
Therefore, Amy, Betty, and Clara spent $435 altogether.