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: number of hearts is 4:3.

She wants to put 5 stars and 4 hearts on each cake.

How many cakes can Liu decorate?

15cakes

Step-by-step explanation:

If liu has 140shapes and the ratio of the number of stars: number of hearts is 4:3.

Then the total ratio of shapes = 4+3 = 7

Amount of star shapes = 4/7 * 140

= 80star shapes

Amount of hearts = 3/7 * 140

= 60heart shapes

If she wants to put 5 stars and 4 hearts on each cake.

Number of cakes with 5stars = 80/5

= 16cakes

Number of cakes with 4hearts = 60/4 = 15cakes

Since the amount of cake that can have 4hearts is lower than that of cakes with 5stars, this means one of the cake won't have 4hearts.

Therefore the total number of cakes she can decorate with 5stars and 4hearts is only 15cakes.