Question

Liu wants to decorate some cakes with shapes.

She has 140 shapes.
Each shape is a star or a heart.
The ratio of the number of stars : to hearts is 4:3.
She wants to put 5 stars and 4 hearts on each cake.
How many cakes can Liu decorate?
Show full working to support your answer.​

Answer 1

15 cakes can be decorated.

Explanation:

Given:

Total number of shapes Liu has = 140

Ratio of shape of stars and hearts = 4 : 3

According to the question:

Each cake have 5 stars and 4 hearts.

Let the number of starts be "4x" and number of hearts be "3x" from the ratio.

Now,

⇒
`4x+3x=140`

⇒
`7x=140`

⇒
`x=(140)/(7)`

⇒
`x=20`

Number of stars =
`4x =4(20) =80`

Number of hearts =
`3x=3(20)=60`

Each cake have 5 stars and 4 hearts .

How many cakes can be decorated with 80 stars.

⇒ No.of cakes = Total number of stars / 5

⇒
`C=(80)/(5)`

⇒
`C=16`

How many cakes can be decorated with 60 hearts.

⇒
`C=(60)/(4)`

⇒
`C=15`

But both shapes are in combination so only 15 cakes can be decorated with the combination of 5 stars and 4 hearts.

Liu can decorate 15 cakes and only.