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A salesman earns a basic salary of €150 per week - Leaving Cert Mathematics - Question 6 - 2017
Question 6
A salesman earns a basic salary of €150 per week. In addition, he gets commission of 20% on sales up to the value of €1000 in the week and 30% commission on any sale... show full transcript
Worked Solution & Example Answer:A salesman earns a basic salary of €150 per week - Leaving Cert Mathematics - Question 6 - 2017
Step 1
Find his total income for a week when his total sales amount to €3000.
Answer
To find the total income:
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Calculate the commission for the first €1000:
Commission = 20% of €1000 = 0.20 × 1000 = €200
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Calculate the sales amount above €1000:
Sales above €1000 = €3000 - €1000 = €2000
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Calculate the commission for the remaining €2000:
Commission = 30% of €2000 = 0.30 × 2000 = €600
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Total commission = €200 (first €1000) + €600 (next €2000) = €800
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Now add the basic salary to find total income:
Total Income = Basic Salary + Total Commission = €150 + €800 = €950
Step 2
Find his total sales for this week.
Answer
Let the total sales be represented as S.
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From the given total income:
Income = Basic Salary + Commission
€1160 = €150 + Commission
This gives:
Commission = €1160 - €150 = €1010
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Since the commission structure is:
- 20% on the first €1000
- 30% on sales above €1000
Calculate how much sales correspond to a €1010 commission:
Step 1: First, find the commission from the first €1000:
Commission from first €1000 = 20% of €1000 = €200
Step 2: Remaining commission = Total Commission - Commission from €1000:
Remaining Commission = €1010 - €200 = €810
Step 3: This remaining commission comes from the sales above €1000:
Since this is at a rate of 30%, we can find the sales above €1000:
Sales above €1000 = Remaining Commission / 30% = €810 / 0.30 = €2700
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Therefore, total sales S will be:
Total Sales = €1000 + €2700 = €3700