Miss Jessica went to the supermarket with a sum of money. She spent 1/2 of her money plus $12 on a cake. She then spent 1/2 of the remaining money plus $7 on drinks. Finally, she spent 1/2 of what was left plus $3.50 on fruits and was left with $6.20. How much money did she spend on drinks? How much money did she have at first?
start with x
spent x/2 + 12, leaving x/2 - 12
spent (x/2 - 12)/2 + 7 = x/4 + 1, leaving x/4 - 13
spent (x/4 - 13)/2 + 7/2 = x/8 - 3, leaving x/8 - 10
so, x/8 - 10 = 6.20
x = 129.60
check:
spent 76.80 on cake, leaving 52.80
spent 33.40 on drinks, leaving 19.40
spent 13.20 on fruit, leaving 6.20
To find out how much money Miss Jessica spent on drinks and how much money she had at first, we can work step by step through the given information.
Let's assign a variable to the amount of money Miss Jessica had at first. Let's call it "x".
Based on the information given, we can break down the problem into multiple steps:
Step 1: She spent 1/2 of her money plus $12 on a cake.
This can be expressed as: x/2 + $12.
Step 2: She spent 1/2 of the remaining money plus $7 on drinks.
Since she spent 1/2 of the remaining money, we need to subtract the amount spent on the cake from the total money she had. The remaining money is (x - x/2 - $12). Therefore, the amount spent on drinks can be expressed as: 1/2 * (x - x/2 - $12) + $7.
Step 3: She spent 1/2 of what was left plus $3.50 on fruits and was left with $6.20.
Again, we need to subtract the amount spent on drinks from the remaining money. The remaining money is (x - x/2 - $12 - 1/2 * (x - x/2 - $12) - $7). Therefore, we can set up the equation:
1/2 * (x - x/2 - $12 - 1/2 * (x - x/2 - $12) - $7) + $3.50 = $6.20.
Now, we can solve the equation to find the value of x, which represents the initial amount of money Miss Jessica had.
1/2 * (x - x/2 - $12 - 1/2 * (x - x/2 - $12) - $7) + $3.50 = $6.20.
Simplifying this equation, we have:
1/2 * (x - x/2 - $12 - 1/2 * (x - x/2 - $12)) + $3.50 = $6.20.
Now, let's solve the equation to find the value of x.