Photo AI
Liu wants to decorate some cakes with shapes - OCR - GCSE Maths - Question 9 - 2018 - Paper 1
Question 9
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... show full transcript
Worked Solution & Example Answer:Liu wants to decorate some cakes with shapes - OCR - GCSE Maths - Question 9 - 2018 - Paper 1
Step 1
Calculate the parts of the ratio
Answer
The ratio of stars to hearts is 4:3. This means that for every 7 shapes (4 stars + 3 hearts), 4 shapes are stars and 3 shapes are hearts. Thus, we can compute the total number of stars and hearts of Liu's 140 shapes as follows:
Let the number of parts be:
- Stars: 4x
- Hearts: 3x
So, we have:
4x + 3x = 140 7x = 140
To find x:
x = \frac{140}{7} = 20
Now substituting back to find stars and hearts:
- Stars: 4x = 4 * 20 = 80
- Hearts: 3x = 3 * 20 = 60
Step 2
Step 3
Determine the number of cakes Liu can decorate
Answer
To find out how many cakes Liu can decorate, we divide the total number of shapes by the total shapes used per cake:
Number of cakes = \frac{Total shapes}{Shapes per cake} = \frac{140}{9}
Performing the division gives: Number of cakes = 15.555...
Since she cannot decorate a fraction of a cake, Liu can decorate a total of 15 cakes.