During a trip, Sally spent 1/4 of her money on some clothes. She also spent 1/3 of the remaining money on a bag. She then bought a camera which cost $15 more than the bag and had $95 left. How much money did Sally have at first?
at the start, she had x dollars.
clothes: x/4
bag: (3x/4)/3 = x/4
camera: bag+15 = x/4+15
remainder: 95
x - x/4 - x/4 - (x/4+15) = 95
x/4 - 15 = 95
x/4 = 110
x = 440
So, she started out with $440
clothes: 110, now has 330
bag: 1/3(330) = 110, now has 220
camera: 125, now has 95
Let's work through this step by step:
1. Let's assume Sally's initial amount of money is "x".
2. Sally spent 1/4 of her money on clothes, so she spent (1/4)x.
3. After buying the clothes, Sally had (3/4)x left.
4. Sally then spent 1/3 of the remaining money on a bag, so she spent (1/3)(3/4)x = (1/4)x on the bag.
5. After buying the bag, Sally had now (3/4)x - (1/4)x = (2/4)x = (1/2)x left.
6. The camera cost $15 more than the bag, so the price of the camera was (1/4)x + $15.
7. After buying the camera, Sally had (1/2)x - [(1/4)x + $15] = $95 left.
8. Let's solve the equation (1/2)x - (1/4)x - $15 = $95:
(1/2 - 1/4)x - $15 = $95
(2/4 - 1/4)x - $15 = $95
(1/4)x - $15 = $95
(1/4)x = $110
x = $110 * 4
x = $440
Therefore, Sally had $440 at first.
To solve this problem, let's start by defining a variable for the amount of money Sally had at first.
Let's say Sally had x dollars at the beginning of her trip.
According to the problem, Sally spent 1/4 of her money on clothes. This means she had 3/4 of her money left.
So, the amount of money she had remaining after buying clothes is (3/4)x.
Next, Sally spent 1/3 of the remaining money on a bag. This means she had 2/3 of (3/4)x = (2/3)(3/4)x = (6/12)x = (1/2)x left.
Now, the problem states that she bought a camera which cost $15 more than the bag. Let's say the cost of the bag was y dollars. So, the cost of the camera was y + $15.
After buying the camera, Sally had $95 left. Therefore, we can set up the following equation:
(1/2)x - (y + $15) = $95
Now we have two equations:
(1/2)x - (y + $15) = $95
(1/2)x = y + $15 + $95
Simplifying the second equation:
(1/2)x = y + $110
Now, we can substitute the second equation into the first equation:
y + $110 - (y + $15) = $95
Simplifying the equation:
$110 - $15 = $95
So, the equation holds true.
To find the value of x, we need to solve this equation:
(1/2)x = y + $110
Therefore, we can conclude that Sally had $110 at first.