Can I really use ALL the candles? I always have one white candle left!!!

Question

2. Bilal is making sets of three candles.

He puts a white candle, a silver candle and
a gold candle into each set.

The candles are sold in packets of different sizes.

There are

25 white candles in a packet
12 silver candles in a packet
and 8 gold candles in a packet.

Bilal wants to use all the candles he buys.

(i) What is the smallest number of packets of white candles, of silver candles and of gold candles he needs to buy?














.............................................. packets of white candles

.............................................. packets of silver candles

.............................................. packets of gold candles


(ii) How many sets of candles can Bilal make from the packets of candles he buys?

Answer 1

Hi, David.

 

For the first part of this problem, you want to find the least common factor of the three numbers provided.

 

You can do it the slow way or the fast way.

 

The slow way is listing the factors of each number until you find the smallest number that all 3 lists has in common. E.g.,

 

8, 16, 24, ... 600

12, 24, 36, ... 600

25, 50, 75, ... 600

 

Or, the fast way involves breaking each number into prime factors, then selecting each factor that appears once or more. If a factor appears more than once, select that factor in the instance in which it has the highest exponent. Then, multiply the factors you selected.

 

So,

8 = 2 * 2 * 2 or 2^3

12 = 2 * 2 * 3 or 2^2 * 3

25 = 5 * 5 or 5^2

 

So, our LCF = 2^3 * 3 * 5^2 = 8 * 3 * 25 = 600.

 

Note, even though 2 appears in both 8 & 12, I selected 2^3 because 12 can gain a two faster than 8 can lose a two.

 

In order to have 600 white, silver, and gold candles, Bilal must buy

 

600/25 or 24 packets of white candles

600/12 or 50 packets of silver candles

600/8 or 75 packets of gold candles

 

With 600 of each candle, he can make 600 sets of candles.