lorinda is given pocket money for a week she decides to spend 2/5 of the money on breakfast, 1/6 of the remaining on snack and 3/4 of what is still remaining on lunch for a day. if she will be left with Gh¢ 100.00 after the first day of making the above expenses,
i. how much money does she have as pocket money
ii. if she is follow the daily budget above, would the money be sufficient for the week
starting amount --- x
after spending 2/5 of it on breakfast, amount left = 3x/5
spends 1/6 of that on snacks, leaving (5/6)(3x/5) = x/2
spends 3/4 of that on lunch leaving with (1/4)(x/2) = x/8
so x/8 = 100
x = 800
To solve this problem, we will start by determining how much money Lorinda had initially as pocket money, and then calculate whether the money would be sufficient for the week. Let's break down the steps:
i. Determining the initial pocket money:
1. Lorinda spends 2/5 of the money on breakfast.
2/5 of the money = 2/5 * Initial Pocket Money
3/5 of the money remaining = (1 - 2/5) * Initial Pocket Money = 3/5 * Initial Pocket Money
2. Lorinda spends 1/6 of the remaining money on snacks.
1/6 of the money = 1/6 * (3/5 * Initial Pocket Money)
5/6 of the money remaining = (1 - 1/6) * (3/5 * Initial Pocket Money) = 5/6 * (3/5 * Initial Pocket Money)
3. Lorinda spends 3/4 of the money remaining on lunch.
3/4 of the money = 3/4 * (5/6 * (3/5 * Initial Pocket Money))
1/4 of the money remaining = (1 - 3/4) * (5/6 * (3/5 * Initial Pocket Money)) = 1/4 * (5/6 * (3/5 * Initial Pocket Money))
After the first day, Lorinda is left with GH¢100.00, so we can set up the following equation:
1/4 * (5/6 * (3/5 * Initial Pocket Money)) = GH¢100.00
Now we can solve for Initial Pocket Money.
ii. Determining if the money would be sufficient for the week:
To determine if the money would be sufficient for the week, we need to compare the remaining balance after the first day with the total pocket money for the week.
1. Calculate the remaining balance after the first day, which is GH¢100.00.
2. Multiply this remaining balance by the number of days in the week (let's assume 7 days) to find the total pocket money for the week.
Total Pocket Money = GH¢100.00 * 7
3. Compare the Total Pocket Money for the week with the initial pocket money calculated in part i. If the Total Pocket Money is greater than or equal to the initial pocket money, then the money would be sufficient for the week. If it is less, then the money would not be sufficient.
You can now go ahead and solve the equations to find the values for the initial pocket money and determine if it would be sufficient for the week.
To solve this problem, we'll step-by-step calculate how much money Lorinda has as pocket money and determine if it's enough for the week.
Let's denote the original pocket money as P.
i. To find out how much money Lorinda has as pocket money, we need to reverse the expenses made on the first day.
1. She spends 3/4 of what is still remaining on lunch for a day. So, after the lunch expense, she has 1 - 3/4 = 1/4 of the remaining money.
This 1/4 of the remaining money is equal to Gh¢ 100.00.
So, let's set up the equation: (1/4) * P = Gh¢ 100.00
To solve for P, we multiply both sides of the equation by 4/1:
P = (4/1) * Gh¢ 100.00
P = Gh¢ 400.00
Therefore, Lorinda originally had Gh¢ 400.00 as pocket money.
ii. To determine if the money is sufficient for the week, we need to find out how much money she spends in total for a week.
1. Lorinda spends 2/5 of the money on breakfast, which is (2/5) * Gh¢ 400.00 = Gh¢ 160.00.
2. After the breakfast expense, she has Gh¢ 400.00 - Gh¢ 160.00 = Gh¢ 240.00 remaining.
3. She spends 1/6 of the remaining money on snack, which is (1/6) * Gh¢ 240.00 = Gh¢ 40.00.
4. After the snack expense, she has Gh¢ 240.00 - Gh¢ 40.00 = Gh¢ 200.00 remaining.
5. She spends 3/4 of the remaining money on lunch, which is (3/4) * Gh¢ 200.00 = Gh¢ 150.00.
6. After the lunch expense, she has Gh¢ 200.00 - Gh¢ 150.00 = Gh¢ 50.00 remaining.
So, after the first day, Lorinda has Gh¢ 50.00 remaining out of her pocket money. Since this amount is less than Gh¢ 100.00, it implies that the money won't be sufficient for the week.
Therefore, the answer is:
i. Lorinda originally had Gh¢ 400.00 as pocket money.
ii. No, the money won't be sufficient for the week.