Party, three friends, Ashley, Cole, and Lauren, shared a big tub of popcorn. Within 30 min, the tub was empty. Ashley ate \frac{5}{24} of the tub while Lauren ate only \frac{1}{8} of the tub. How much did Cole eat?
The Correct Answer and Explanation is:
To determine how much Cole ate, we need to know how much of the tub was consumed by Ashley and Lauren, and then subtract that from the total amount of the tub.
Step 1: Find the amount eaten by Ashley and Lauren
- Ashley ate 524\frac{5}{24}245 of the tub.
- Lauren ate 18\frac{1}{8}81 of the tub.
First, let’s express Lauren’s portion as a fraction with the same denominator as Ashley’s portion. To do this, we need to rewrite 18\frac{1}{8}81 with a denominator of 24:18=324\frac{1}{8} = \frac{3}{24}81=243
Now, we can find the total amount eaten by Ashley and Lauren by adding their portions together:524+324=824\frac{5}{24} + \frac{3}{24} = \frac{8}{24}245+243=248
Step 2: Subtract Ashley and Lauren’s portions from the whole tub
The whole tub represents 1, or 2424\frac{24}{24}2424. Now, subtract the amount eaten by Ashley and Lauren:2424−824=1624\frac{24}{24} – \frac{8}{24} = \frac{16}{24}2424−248=2416
Step 3: Simplify the fraction
1624\frac{16}{24}2416 simplifies to 23\frac{2}{3}32 when we divide both the numerator and the denominator by their greatest common divisor (which is 8).
Thus, Cole ate 23\frac{2}{3}32 of the tub.
Conclusion:
Cole ate 23\frac{2}{3}32 of the tub of popcorn.
