In one store, the ratio of DVDs to videos is 7:5. In another store, the ratio of DVDs to videos is 4:3. Explain why you cannot say which store has more DVDs.
compare 7:5 to 40:30
or, 70:50 to 4:3
the size of the ratio says nothing about the total quantities
To determine which store has more DVDs, we need to compare the actual quantities of DVDs in each store. Ratios provide a relative comparison, but they are not enough to determine the actual quantities.
In the first store, the ratio of DVDs to videos is 7:5, meaning that for every 7 DVDs, there are 5 videos. Let's say we have 7 units of DVDs and 5 units of videos. This ratio can be scaled up or down while maintaining the same relative comparison. For example, if we double the quantities, we would have 14 DVDs and 10 videos, which still represents a 7:5 ratio.
The same logic applies to the second store where the ratio is 4:3. We could have 4 units of DVDs and 3 units of videos or any multiple of those quantities.
While the ratio gives us insight into the relationship between DVDs and videos within each store, without knowing the actual quantities, we cannot determine which store has more DVDs. To determine that, we would need additional information, such as the actual number of DVDs in each store.