Question

Spring flowering bulbs are on sale at austin's garden shop. Travis and sydney want to buy equal amounts of all four kinds. What is the least number of each kind they can buy?

Answer 1

Answer:

60

Step-by-step explanation:

The problem will be solved by looking for the least common multiple (LCM) of the amounts of all four kinds since they want equal amounts of each.

LCM is defined as the smallest positive integer that is divisible by each of the integers (spring flowering bulbs in this case) involved in the operation.

therefore, we are looking for the LCM of the following integers:

Crocus: 6

Tulip: 4

Daffodil: 3

Hyacinth: 5

The first step to calculate the LCM is to factor each integer (to break it up into numbers that can be multiplied together to get the original number) and express them in terms of powers:

Crocus: 6=2*3

Tulip: 4=2*2=$2^{2}$

Daffodil 3 = 3 (prime numbers only have themselves as factors)

Hyacinth 5=5 (prime numbers only have themselves as factors)

Now, To calculate the LCM we need to multiply all factors we have found ( in this case 2, 3, and 5) but only once and with the maximum power.

$LCM=2^{2} *3*5=4*3*5=60$

This means the least number of each spring flowering bulbs that they can buy to buy equal amounts is 60.

Now this will cost:

Crocus: $\frac{60}{6}*1.65 =10*1.65=16.5$

Tulip: $\frac{60}{4}*3.50 =15*3.50=52.5$

Daffodil: $\frac{60}{3}*1.95 =20*1.95=39$

Hyacinth: $\frac{60}{5}*2.25 =12*2.25=27$