Middle School

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Joseph put candles on a cake. He lit \(\frac{1}{4}\) of those candles, then he lit five more of the candles on the cake. As a result, exactly \(\frac{1}{3}\) of the candles on the cake were lit. What was the total number of candles on the cake?

Answer :

1/4x + 5 = 1/3x
5 = 1/3x - 1/4x
5 = 4/12x - 3/12x
5 = 1/12x
5 * 12 = x
60 = x....there were 60 candles on the cake

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Rewritten by : Barada

The total number of candles on the cake is 60, which is determined by using LCM.

Let's assume the total number of candles on the cake is represented by "x."

According to the information given:

Joseph lit 1/4 of those candles.

So, the number of candles lit = (1/4) × x = x/4.

He then lit five more candles.

Now, the total number of lit candles = x/4 + 5.

As a result, exactly 1/3 of the candles on the cake were lit.

The number of lit candles = (1/3)x.

Since both statements refer to the same number of lit candles, we can equate them:

x/4 + 5 = (1/3) x

To find the value of "x," let's solve the equation:

Multiply both sides by 12 (LCM of 4 and 3) to eliminate fractions:

12 × (x/4) + 12 × 5 = 12 × (1/3) × x.

3x + 60 = 4x.

Subtract 3x from both sides:

60 = x.

So, the total number of candles on the cake is 60.

To learn more about the Least Common Multiple(LCM) here :

https://brainly.com/question/17256135

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