Thornton Wyatt
11/19/2023 · Middle School
18. For every book Tony sells, he gets \( \$ 1.75 \) as commission. He gets additional \( \$ 1.50 \) for every 8 books sold. How many hooki did Tony ent he eamed \( \$ 50 \) in commission? \( \$ 1.75 \times 8=\$ 1200 \)
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Step-by-step Solution
To find out how many books Tony sold to earn $50 in commission, we can set up an equation based on the given information.
Let's denote the number of books Tony sold as \( x \).
From the given information:
- Tony earns $1.75 for every book sold.
- Tony earns an additional $1.50 for every 8 books sold.
We can express the total commission earned by Tony as:
\[ 1.75x + 1.50 \times \left( \frac{x}{8} \right) = 50 \]
Simplifying the equation:
\[ 1.75x + 0.1875x = 50 \]
\[ 1.9375x = 50 \]
\[ x = \frac{50}{1.9375} \]
Now, we can calculate the value of \( x \) to find out how many books Tony sold to earn $50 in commission.
Calculate the value by following steps:
- step0: Calculate:
\(\frac{50}{1.9375}\)
- step1: Convert the expressions:
\(\frac{50}{\frac{31}{16}}\)
- step2: Multiply by the reciprocal:
\(50\times \frac{16}{31}\)
- step3: Multiply:
\(\frac{50\times 16}{31}\)
- step4: Multiply:
\(\frac{800}{31}\)
Tony sold approximately 25.81 books to earn $50 in commission.
Since Tony cannot sell a fraction of a book, we can round this to the nearest whole number. Therefore, Tony sold 26 books to earn $50 in commission.
Quick Answer
Tony sold 26 books to earn $50 in commission.
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