Sandra spent one-fifth of her money and loaned one-third of the remainder to her brother. She had $24 left. How much did she begin with?
m - 1/5 m = 4/5 m
4/5 m * 1/3 = 4/15 m
m - 1/5 m - 4/15 m = 24
m = 45
When working backwards we first need to deal with 1/3. so since it says 1/3 of the remainder, does this mean to divide 24 by 1/3
if r is the remainder, then
24 = 2/3 r
r = 36
r = 4/5 m, so
m = 5/4 * 36 = 45
I understand thank you.
To solve this problem, let's break it down into steps:
Step 1: Let's assume that Sandra's initial amount of money is represented by "x" dollars.
Step 2: Sandra spent one-fifth of her money, which means she has 4/5 (four-fifths) of her money remaining.
- The amount remaining after spending one-fifth is 4/5 * x dollars.
Step 3: Sandra loaned one-third of the remainder to her brother, which means she has 2/3 (two-thirds) of the remaining amount left after Step 2.
- The amount remaining after lending one-third is 2/3 * (4/5 * x) dollars.
Step 4: According to the problem, Sandra has $24 remaining, which means the amount remaining after Step 3 is equal to $24.
- 2/3 * (4/5 * x) = $24
Step 5: To find the value of "x" (the amount Sandra began with), we can solve the equation from Step 4.
- Multiply both sides of the equation by 15/8 to eliminate the fractions:
(2/3 * (4/5 * x)) * (15/8) = $24 * (15/8)
(2/3 * 4/5 * x) * (15/8) = $24 * (15/8)
- Simplify the equation:
(8/15 * 2/3 * 4/5 * x) = $24 * (15/8)
(16/15 * 4/5 * x) = $24 * (15/8)
(64/75 * x) = $180
- Divide both sides of the equation by 64/75 to solve for "x":
x = ($180) / (64/75)
- Simplify the expression on the right-hand side:
x = $180 * (75/64)
- Calculate the final answer:
x = $210.94 (rounded to the nearest cent)
Therefore, Sandra began with approximately $210.94.