A student had an amount of $P at the beginning of a semester. He spent 1/3 of the amount on books and 3/5 of the remainder on snacks. If $400.00 was left at the end of the semester , find the value of P.
1 had P
2 spent 1P/3 on books, 2P/3 left
3 spent 3/5 * 2P/3 = 2 P/5 on snacks 2/5 * 2 P/3 = 4 P/15 left
so
4 P/15 = 400
P = 1500
2/3P - .6P = 400
Solve for P.
Let's solve this problem step-by-step:
Step 1: Let's represent the amount the student had at the beginning of the semester as P.
Step 2: The student spent 1/3 of the amount on books, which means he had 2/3 of the amount remaining.
Step 3: The student then spent 3/5 of the remainder on snacks, leaving him with 2/5 of the remainder.
Step 4: We are given that $400.00 was left at the end of the semester, which represents 2/5 of the remainder. So we can set up an equation:
2/5 * P = $400.00
Step 5: To solve for P, we will multiply both sides of the equation by 5/2:
(2/5 * P) * (5/2) = $400.00 * (5/2)
Step 6: Simplifying both sides of the equation gives us:
P = $400.00 * (5/2) / (2/5)
Step 7: Simplifying further, we have:
P = $400.00 * (5/2) * (5/2) / 2
Step 8: Multiplying and simplifying:
P = $400.00 * (25/4) / 2
P = $400.00 * 25/8
Step 9: Multiplying and simplifying:
P = $5000.00 / 8
Step 10: Dividing:
P = $625.00
Therefore, the value of P, or the amount the student had at the beginning of the semester, is $625.00.
To find the value of P, we need to work backward from the given information. Let's break down the problem step by step:
Step 1: The student spent 1/3 of the amount on books.
This means the student has 2/3 of the original amount remaining. Let's call this remainder R.
Step 2: The student spent 3/5 of the remainder on snacks.
This means the student has 2/5 of the remainder remaining. Let's call this new remainder S.
Step 3: At the end of the semester, $400.00 was left.
This means the value of the new remainder S is $400.00. We can set up an equation: S = $400.00.
Step 4: Calculate the value of P.
To find the value of P, we need to calculate the original amount before any expenses were made. We can work backward from the remaining amount.
Since S represents 2/5 of the original amount P, we can set up an equation: S = (2/5)P.
Using the equation from Step 3, we can substitute S with $400.00: $400.00 = (2/5)P.
To solve for P, we need to isolate it on one side of the equation. We can multiply both sides of the equation by 5/2 to get rid of the fraction:
($400.00) * (5/2) = (2/5)P * (5/2).
$2000.00 = P.
Therefore, the value of P is $2000.00.