Can anyone explain wat they mean when they say The 4-pound bucket dumps out more frequently than the 7-pound bucket, and the ratio of number of dumps is the same as the ratios of their sizes.
We are given that the larger bucket dumps out 112 times per day, so the smaller bucket dumps out
times per day.
@amiablehummingbird Good question!
So, both buckets are being filled up at the same rate. But, since the 4-pound bucket holds less, it's going to dump more often than the 7-pound bucket. How much more often? Well, since the 4-pound bucket is \(\frac47\) of the size of the 7-pound, it's going to have to dump \(\frac74\) as often in order to take the same amount of corn.
Thus, since it dumps \(\frac74\) more often, \(\frac74\cdot112\) is the answer.
Let me know if this makes sense!