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
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
