Ingrid offered to pay her brother $2 for doing her share
of the housework each day, but fined him $5 if he forgot to
do it. After 4 weeks, Ingrid discovered that she did not owe
her brother any money. For how many days did Ingrid’s
brother do her share of the housework?
Let's approach this problem step-by-step:
Step 1: Calculate the total amount of money Ingrid would have paid her brother if he had done her share of the housework every day.
Since Ingrid offered $2 for each day her brother did her share of the housework, the total amount of money Ingrid would have paid her brother is 2 * (the number of days her brother did her share).
Step 2: Calculate the total amount of money Ingrid fined her brother if he forgot to do her share of the housework.
Since Ingrid fined her brother $5 for each day he forgot to do her share, the total amount of money Ingrid fined her brother is 5 * (the number of days her brother forgot to do her share).
Step 3: Set up the equation based on the given information and solve for the number of days her brother did her share.
According to the problem, the total amount of money Ingrid owes her brother is 0 (since she discovered she did not owe him any money). Thus, we can set up the equation:
Total money paid by Ingrid - Total money fined = 0
(2 * number of days her brother did her share) - (5 * number of days her brother forgot to do her share) = 0
Step 4: Simplify the equation and solve for the number of days her brother did her share.
2 * number of days her brother did her share - 5 * number of days her brother forgot to do her share = 0
2 * number of days her brother did her share = 5 * number of days her brother forgot to do her share
number of days her brother did her share = (5 * number of days her brother forgot to do her share) / 2
Given that Ingrid discovered she did not owe her brother any money after 4 weeks, which is equal to 28 days, we can substitute 28 for the total number of days her brother did her share and solve for the number of days her brother forgot:
number of days her brother did her share = (5 * number of days her brother forgot) / 2
28 = (5 * number of days her brother forgot) / 2
56 = 5 * number of days her brother forgot
number of days her brother forgot = 56 / 5
number of days her brother forgot = 11.2
However, since we are dealing with days, the number of days her brother forgot must be a whole number. Therefore, we round 11.2 down to the nearest whole number, which is 11.
Step 5: Calculate the number of days her brother did her share by subtracting the number of days her brother forgot from the total number of days (28):
number of days her brother did her share = total number of days - number of days her brother forgot
number of days her brother did her share = 28 - 11
number of days her brother did her share = 17
Therefore, Ingrid's brother did her share of the housework for 17 days.
To solve this problem, we can use the fact that Ingrid doesn't owe her brother any money after 4 weeks. Let's break it down step by step:
1. Calculate the total money Ingrid would have to pay her brother if he did the housework every day for 4 weeks:
- Ingrid would pay her brother $2 every day if he did the housework.
- Since there are 7 days in a week, Ingrid would owe her brother $2 x 7 = $14 per week.
- In 4 weeks, Ingrid would owe her brother $14 x 4 = $56 in total.
2. Calculate the total money Ingrid would have to fine her brother if he forgot to do the housework every day for 4 weeks:
- Ingrid would fine her brother $5 every day if he forgot to do the housework.
- Since there are 7 days in a week, Ingrid would fine her brother $5 x 7 = $35 per week.
- In 4 weeks, Ingrid would fine her brother $35 x 4 = $140 in total.
3. Calculate the net amount owed by Ingrid to her brother:
- Subtract the total fine amount from the total payment amount: $56 (payment) - $140 (fine) = -$84.
- Since the result is negative, it means Ingrid's brother actually owes her $84.
From this, we can conclude that Ingrid's brother did not do her share of the housework for any days during the 4 weeks.