Question

the residents of a city voted on whether to raise property taxes. the ratio of yes votes to no votes was 5 to 7. if there were 8292 total votes, how many yes votes were there?

Explanation:

Step1: Determine total parts of ratio

The ratio of yes to no votes is \(5:7\), so total parts \(= 5 + 7 = 12\).

Step2: Find value of one part

Total votes \(= 8292\), so one part \(= \frac{8292}{12} = 691\).

Step3: Calculate no votes

No votes correspond to 7 parts, so no votes \(= 7\times691 = 4837\). Wait, wait, maybe the question is about yes votes? Wait, let's re - check. Wait, the ratio is yes to no \(5:7\), total votes 8292. Wait, maybe I misread. Wait, let's do it again. Total parts \(5 + 7=12\). Value of one part: \(8292\div12 = 691\). If we want no votes (7 parts): \(7\times691 = 4837\). If yes votes (5 parts): \(5\times691 = 3455\). Wait, maybe the original problem was "how many no votes" or "how many yes votes". Wait, the image text: "The residents of a city voted on whether to raise property taxes. The ratio of yes votes to no votes was 5 to 7. If there were 8292 total votes, how many..." So let's solve for no votes (since ratio yes:no = 5:7). So total parts 12. One part: \(8292\div12 = 691\). No votes: \(7\times691 = 4837\). Wait, but maybe the question was yes votes? Wait, 5 parts: \(5\times691 = 3455\). Wait, let's check the arithmetic. \(12\times691 = 8292\) (since \(12\times600 = 7200\), \(12\times91 = 1092\), \(7200 + 1092 = 8292\)). So if ratio yes:no = 5:7, yes votes \(= 5\times691 = 3455\), no votes \(= 7\times691 = 4837\).

Answer:

If the question is about no votes, the answer is \(4837\); if about yes votes, the answer is \(3455\). (Assuming the question is to find no votes as per the ratio's second part, the answer is \(4837\))