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26 Apr 2026, 11:27
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Three freelance designers, Luca, Sophie, and Marta, receive monthly retainers that total €9,700. Luca spends 70% of his retainer, Sophie spends 75%, and Marta spends 60%. At the end of the month, their savings are in the ratio 9:8:14. What is Marta’s monthly retainer?
A. €3,000
B. €3,200
C. €3,500
D. €3,700
E. €4,000
A. €3,000
B. €3,200
C. €3,500
D. €3,700
E. €4,000
26 Apr 2026, 11:27
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Official Solution:
Three freelance designers, Luca, Sophie, and Marta, receive monthly retainers that total €9,700. Luca spends 70% of his retainer, Sophie spends 75%, and Marta spends 60%. At the end of the month, their savings are in the ratio 9:8:14. What is Marta’s monthly retainer?
A. €3,000
B. €3,200
C. €3,500
D. €3,700
E. €4,000
Let \(L\), \(S\), \(M\) be the retainers.
• Savings:
Luca saves 30%, so savings = \(0.30L\)
Sophie saves 25%, so savings = \(0.25S\)
Marta saves 40%, so savings = \(0.40M\)
• Given savings ratio \(9:8:14\), set
\(0.30L = 9k\)
\(0.25S = 8k\)
\(0.40M = 14k\)
• Solve each:
\(L = \frac{9k}{0.30} = \frac{9k}{\frac{3}{10}} = 9k * \frac{10}{3} = 30k\)
\(S = \frac{8k}{0.25} = \frac{8k}{\frac{1}{4}} = 8k * 4 = 32k\)
\(M = \frac{14k}{0.40} = \frac{14k}{\frac{2}{5}} = 14k * \frac{5}{2} = 35k\)
• Total retainer:
\(30k + 32k + 35k = 97k = 9700\)
So \(k = 100\)
• Marta’s retainer:
\(M = 35k = 3500\) euros.
Answer: C
Three freelance designers, Luca, Sophie, and Marta, receive monthly retainers that total €9,700. Luca spends 70% of his retainer, Sophie spends 75%, and Marta spends 60%. At the end of the month, their savings are in the ratio 9:8:14. What is Marta’s monthly retainer?
A. €3,000
B. €3,200
C. €3,500
D. €3,700
E. €4,000
Let \(L\), \(S\), \(M\) be the retainers.
• Savings:
Luca saves 30%, so savings = \(0.30L\)
Sophie saves 25%, so savings = \(0.25S\)
Marta saves 40%, so savings = \(0.40M\)
• Given savings ratio \(9:8:14\), set
\(0.30L = 9k\)
\(0.25S = 8k\)
\(0.40M = 14k\)
• Solve each:
\(L = \frac{9k}{0.30} = \frac{9k}{\frac{3}{10}} = 9k * \frac{10}{3} = 30k\)
\(S = \frac{8k}{0.25} = \frac{8k}{\frac{1}{4}} = 8k * 4 = 32k\)
\(M = \frac{14k}{0.40} = \frac{14k}{\frac{2}{5}} = 14k * \frac{5}{2} = 35k\)
• Total retainer:
\(30k + 32k + 35k = 97k = 9700\)
So \(k = 100\)
• Marta’s retainer:
\(M = 35k = 3500\) euros.
Answer: C
06 May 2026, 08:01
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Hi Bunuel,
I understand the approach and the solution.
During the test, I was short on time and utilised this approach. It landed the same answer but I want to know if there is no logical gap.
I used options and found 40% of it as that would be the savings for marta.
As per the ratio; it is a multiple of 14. So, I thought along this and only option C was fit; 3500.
Thank you.
I understand the approach and the solution.
During the test, I was short on time and utilised this approach. It landed the same answer but I want to know if there is no logical gap.
I used options and found 40% of it as that would be the savings for marta.
As per the ratio; it is a multiple of 14. So, I thought along this and only option C was fit; 3500.
Thank you.
Bunuel
