Wendy saves 30% of her income each month. ⅜ of her expenditures is spent on cosmetics, ⅙ of it is spent on transport and ⅖ of the remainder is spent on food. If she spends $469 on cosmetics and food altogether, how much does she save each month?
What does i stand for?
Income = 100% = 100/100 = 1
Saving = 30% = 30/100 = 0.3
Expenditures = 70% = 0.7
Now we are going to calculate the rest
Cosmetics = 3/8 of 70% = 3/8(.7) = 0.2625
Transportation = 1/6 of 70% = 1/6(.7) = 0.1166
Reminder = 1 - (0.3 + 0.2625 + 0.1166) = 0.39086
Food = 2/5 of Reminder = 2/5(0.39086) = 0.4 (0.39086) = 0.156344
So now that we know all the pieces let us calculate her income
We know that she spends $469 on food plus cosmetics so:
f + c = 469
replace f with 0.156344x and c with 0.2625x
0.156344x + 0.2625x = $469
0.41844x = $469
x = 469/0.41844 = $1120
So Wendy makes $1120.83 per month
She saves 30% of her income = .3(1120.83) = $336.25 per month
To calculate how much Wendy saves each month, we need to determine the total amount of her income spent on cosmetics and food combined, and then subtract that from her monthly income.
Let's break down the problem step by step:
Step 1: Calculate expenditures on cosmetics
We are given that ⅜ of Wendy's expenditures are spent on cosmetics. If we represent Wendy's total expenditure as "x," then the amount spent on cosmetics can be calculated as (⅜) * x.
Step 2: Calculate expenditures on transport
We are given that ⅙ of Wendy's expenditures are spent on transport. Following the same logic as above, the amount spent on transport can be represented as (⅙) * x.
Step 3: Calculate total expenses before food
To find the total expenses before food, we subtract the amounts spent on cosmetics and transport from the total expenditure:
Total expenses before food = x - (⅜) * x - (⅙) * x
Step 4: Calculate expenditures on food
We are given that ⅖ of the remainder is spent on food. So, if we represent the remainder after deducting expenses on cosmetics and transport as "y," then the amount spent on food can be calculated as (⅖) * y.
Step 5: Calculate the total expenses on cosmetics and food
We are given that the total expenses on cosmetics and food are $469. Therefore, we can write an equation:
(⅜) * x + (⅖) * y = $469
Step 6: Calculate the remainder after deducting expenses on cosmetics and food
To find the remainder, we can subtract the total expenses on cosmetics and food from the total expenditure:
Remainder = x - [(⅜) * x + (⅖) * y]
Step 7: Calculate Wendy's savings
Given that Wendy saves 30% of her monthly income, we can calculate her savings as:
Savings = (30/100) * [x - [(⅜) * x + (⅖) * y]]
By solving the equations and substituting the given value of total expenses on cosmetics and food ($469) into the equation (⅜) * x + (⅖) * y = $469, we can find the value of Wendy's savings.
Note: The problem does not provide the specific income or values for expenses, so we cannot calculate the exact amount of Wendy's savings without additional information.
f = (2/5) (i - 3i/10 - 3i/8 - i/6) ... find f in terms of i
469 = 3i/8 + f ... substitute for f , then solve for i
s = 3i/10