Question

teks 7.4d
at a flower shop, the ratio of roses to lilies to tulips in a bouquet is 5:3:2. if there are 18 lilies in the bouquet:
how many roses are there?
how many flowers are in the bouquet in total?
a baker decorates 20 cupcakes per hour for the first 3 hours. then, with the help of an assistant, the decorating rate increases to 30 cupcakes per hour for the next 2 hours. how many cupcakes did they decorate in total?

Explanation:

Flower Bouquet Sub - Questions

How many roses are there?

Step1: Find the multiplier

The ratio of roses to lilies to tulips is \(5:3:2\). Let the number of roses, lilies, and tulips be \(5x\), \(3x\), and \(2x\) respectively. We know that the number of lilies is 18, so \(3x = 18\). Solving for \(x\), we divide both sides by 3: \(x=\frac{18}{3}=6\).

Step2: Calculate the number of roses

The number of roses is \(5x\). Substituting \(x = 6\) into \(5x\), we get \(5\times6 = 30\).

Step1: Find the number of tulips

We know \(x = 6\) (from the previous step) and the number of tulips is \(2x\). So, the number of tulips is \(2\times6=12\).

Step2: Calculate the total number of flowers

The total number of flowers is the sum of the number of roses, lilies, and tulips. We have roses = 30, lilies = 18, and tulips = 12. So, total flowers \(=30 + 18+12=60\).

Step1: Calculate cupcakes decorated in the first 3 hours

The baker decorates 20 cupcakes per hour for 3 hours. So, the number of cupcakes decorated in the first 3 hours is \(20\times3 = 60\).

Step2: Calculate cupcakes decorated in the next 2 hours

With the assistant, the rate is 30 cupcakes per hour for 2 hours. So, the number of cupcakes decorated in the next 2 hours is \(30\times2=60\).

Step3: Calculate the total number of cupcakes

To find the total number of cupcakes, we add the number of cupcakes decorated in the first 3 hours and the next 2 hours. So, total cupcakes \(=60 + 60 = 120\).

Answer:

30

How many flowers are in the bouquet in total?