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Answer :
There are 30 candles in total on the cake
There was 1/3 lit and after lighting 5 more 1/2 of the candles were lit
So 5 candles is the difference between 1/3 of all candles and 1/2 of all candles the difference between those two is 1/6 therefor 5 candles is 1/6 of the total candles in the cake
We take 5 x 6 and get 30 for the total number of candles on the cake
There was 1/3 lit and after lighting 5 more 1/2 of the candles were lit
So 5 candles is the difference between 1/3 of all candles and 1/2 of all candles the difference between those two is 1/6 therefor 5 candles is 1/6 of the total candles in the cake
We take 5 x 6 and get 30 for the total number of candles on the cake
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Rewritten by : Barada
The total number of candles on the cake is 30.
Let's denote the total number of candles on the cake as C. According to the problem, Joseph lit [tex]\( \frac{1}{3} \)[/tex] of the candles first, and then he lit 5 more candles. After lighting these additional candles, exactly [tex]\( \frac{1}{2} \)[/tex] of the total candles were lit. We can set up an equation to represent this situation:
[tex]\[ \frac{1}{3}C + 5 = \frac{1}{2}C \][/tex]
To solve for C , we first multiply every term by 3 to eliminate the fraction on the left side of the equation:
[tex]\[ C + 15 = \frac{3}{2}C \][/tex]
Next, we multiply every term by 2 to eliminate the fraction on the right side of the equation:
2C + 30 = 3C
Now, we can subtract 2C from both sides to isolate C:
30 = C
