Exercise 16 Page 38

We want to buy tealight candles and mints as a party favors for a baby shower. The tealight candles come in packs of 12 for $ 3.50 and the mints come in packs of 50 for $ 6.25. We want to calculate the least amount of money we would have to spend in order to buy the same number of each item. To do so, let's start by drawing a factor tree for each number.

The red circles are the prime factors of the given number. We can use these factors to write the prime factorization of each number. 12 &= 2 * 2 * 3 = 2^2 * 3 50&= 2 * 5 * 5 = 2 * 5^2Since we want to have the same number of candles and mints, we can find the least common multiple (LCM) of the numbers. To find this number, we multiply the highest power of each prime factor. LCM= 2^2 * 3 * 5^2 → LCM = 300 This means that we need to buy at least 300 of each item. Now we will divide 300 by 12 and 50 to find the number of packages we should buy in order to have the same number of each item.

We should buy 25 packages of tealight candles and 6 packages of mints in order to have the same number of both for the least amount of money. Next, let's multiply these quantities by the corresponding price of each pack. This will give us the total amount of money we will spend. Total cost of candles=25(3.50) = 87.50 dollars Total cost of mints=6(6.25) = 37.50 dollars Finally, we will add the cost of each item to find the total cost. Total cost = 87.50+ 37.50= 125 dollars We need to spend $ 125 to buy the smallest quantity fo the same number of candles and mints.