Answer:
15 cakes can be decorated.
Step-by-step 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,
⇒ [tex]4x+3x=140[/tex]
⇒ [tex]7x=140[/tex]
⇒ [tex]x=\frac{140}{7}[/tex]
⇒ [tex]x=20[/tex]
Number of stars = [tex]4x =4(20) =80[/tex]
Number of hearts = [tex]3x=3(20)=60[/tex]
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
⇒ [tex]C=\frac{80}{5}[/tex]
⇒ [tex]C=16[/tex]
How many cakes can be decorated with 60 hearts.
⇒ [tex]C=\frac{60}{4}[/tex]
⇒ [tex]C=15[/tex]
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.
