How can I solve this: Sandy decided to give one-fourth of her CDs to Jenn. Then she gives one-half of the remaining CDs to Bob. If she is left with 6 CDs,how many CDs did she have to begin with?
let the number she had be x
x - (1/4)x - (1/2)(3/4)x = 6
x - x/4 - 3x/8 = 6
times 8
8x - 2x - 3x = 48
3x = 48
x = 16
She had 16 CDs
check:
she had 16, gave 1/4 away
leaving her with 12
she gave 1/2 of those away, so she gave 6 of the remaining 12 away, leaving her with 6
-all checks out!
To solve this problem, we need to work backwards. Let's go step by step:
Step 1: Sandy is left with 6 CDs.
Step 2: She gives one-half of the remaining CDs to Bob.
Step 3: After giving half to Bob, she is left with 6 CDs.
Step 4: Let's determine how many CDs she had after Step 2 (before giving half to Bob).
Given that she is left with 6 CDs after Step 2, we know that these 6 CDs represent half of what she had before giving CDs to Bob. So, if 6 CDs represent half, then the full amount before giving CDs to Bob must be twice that amount.
Therefore, the number of CDs she had before giving CDs to Bob is 6 CDs x 2 = 12 CDs (Step 4).
Now let's move to Step 1:
Step 1: Sandy decided to give one-fourth of her CDs to Jenn. If she is left with 12 CDs (as we found in Step 4), we need to determine how many CDs she had before giving CDs to Jenn.
Given that she is left with 12 CDs after Step 1, we know that these 12 CDs represent three-fourths (3/4) of what she had before giving CDs to Jenn. So, if 12 CDs represent three-fourths, then the full amount before giving CDs to Jenn must be four times that amount.
Therefore, the number of CDs she had before giving CDs to Jenn is 12 CDs x 4 = 48 CDs.
Therefore, Sandy had a total of 48 CDs to begin with.