Olivia bought some school supplies. In the first store she spent half the money she had plus $6. In the second store she spent one third of what was left plus $6.In the last store she spent ¼ of what was left and came home with $6.How much did she start out with?
she started with x
after store 1, she had x/2-6
after store 2, she had (x/2-6)* 2/3 - 6
after store 3, she had ((x/2-6)* 2/3 - 6)* 3/4 = 6
((x/3)-4-6)* 3/4 = 6
(x/3 - 10) = 8
x/3 - 10 = 8
x/3 = 18
x = 54
So, she started out with $54
At store 1, she spent 27+6 = 33, leaving $21
At store 2, she spent 7+6=13, leaving $8
At store 3 she spent 2, leaving $6
To find out how much Olivia started with, we can work backwards from the last store. Let's go through it step by step:
Step 1: Olivia came home from the last store with $6.
Step 2: In the last store, she spent 1/4 of what was left.
Step 3: Let's say she had X dollars left before going to the last store.
Step 4: Olivia spent 1/4*X in the last store.
Step 5: After spending 1/4*X, she came home with $6.
Step 6: So, 1/4*X = $6.
We can solve this equation to find the value of X. Let's multiply both sides of the equation by 4 to get rid of the fraction:
1/4*X * 4 = $6 * 4
X = $24
Therefore, before going to the last store, Olivia had $24.
Now, let's find out how much money she had before going to the second store:
Step 7: Olivia spent 1/4*X in the last store, which is 1/4*$24 = $6.
Step 8: So, before going to the last store, Olivia had $24 + $6 = $30.
Next, let's calculate how much money she had before going to the first store:
Step 9: In the second store, she spent one third of what was left plus $6.
Step 10: Let's say she had Y dollars left before going to the second store.
Step 11: Olivia spent 1/3*Y in the second store, which is Y/3.
Step 12: After spending Y/3, she had $30 left.
Step 13: So, Y/3 = $30.
To find the value of Y, let's multiply both sides of the equation by 3:
Y/3 * 3 = $30 * 3
Y = $90
Therefore, before going to the second store, Olivia had $90.
Now, let's calculate how much money she had at the beginning:
Step 14: Olivia spent half the money she had plus $6 in the first store.
Step 15: Let's say she had Z dollars at the beginning.
Step 16: Olivia spent 1/2*Z in the first store, which is Z/2.
Step 17: After spending Z/2, she had $90 left.
Step 18: So, Z/2 = $90.
To find the value of Z, let's multiply both sides of the equation by 2:
Z/2 * 2 = $90 * 2
Z = $180
Therefore, Olivia started with $180.