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Andrew, Brandon and Cosmo are the first three batters in the school cricket team - HSC - SSCE Mathematics Standard - Question 18 - 2019 - Paper 1
Question 18
Andrew, Brandon and Cosmo are the first three batters in the school cricket team. In a recent match, Andrew scored 30 runs, Brandon scored 25 runs and Cosmo scored 4... show full transcript
Worked Solution & Example Answer:Andrew, Brandon and Cosmo are the first three batters in the school cricket team - HSC - SSCE Mathematics Standard - Question 18 - 2019 - Paper 1
Step 1
What is the ratio of Andrew’s to Brandon’s to Cosmo’s runs scored, in simplest form?
Answer
To find the ratio of Andrew’s, Brandon’s, and Cosmo’s runs, we start with their respective scores:
- Andrew: 30 runs
- Brandon: 25 runs
- Cosmo: 40 runs
The initial ratio is:
To simplify this ratio, we find the greatest common divisor (GCD) of the numbers, which is 5:
- For Andrew: (30 ÷ 5 = 6)
- For Brandon: (25 ÷ 5 = 5)
- For Cosmo: (40 ÷ 5 = 8)
Thus, the simplest form of the ratio is:
Step 2
How many runs were scored by the whole team?
Answer
From the question, the ratio of total runs scored by Andrew, Brandon, and Cosmo to the total runs scored by the whole team is given as 19:36.
First, we calculate the total runs scored by Andrew, Brandon, and Cosmo:
Let (x) be the total number of runs scored by the whole team. According to the given ratio:
Cross-multiplying gives:
Calculating the right side:
By dividing both sides by 19, we find:
Therefore, the total runs scored by the whole team is:
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