To find real-life situations that fit the equation \( 8(x + 9) = 144 \), we'll first solve the equation for \( x \).
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Distribute the 8: \[ 8x + 72 = 144 \]
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Subtract 72 from both sides: \[ 8x = 72 \]
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Divide by 8: \[ x = 9 \]
Now that we know \( x = 9 \), here are some real-life situations that might correspond to this equation:
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Group Projects: A teacher assigns a project to a class where each student contributes equally. Each student is currently bringing in 9 items, and the total number of items from the entire group should be 144 when 8 groups of students combine their items.
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Fitness Training: A personal trainer is designing a workout plan. The plan includes a base workout of 9 minutes plus an additional workout that is done in 8 different segments. The total time spent working out, which includes warm-up and cool down, should be 144 minutes.
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Cooking Portions: A chef is preparing meals for a catering event. Each meal requires a base of 9 ingredients, and the chef decides to prepare 8 meals. If the total number of ingredients used for all meals is supposed to be 144, this fits the equation.
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Discount Pricing: In a store sale, a customer finds that when they buy 8 pairs of socks, each pair costing \( x + 9 \) dollars (where \( x \) is the unknown discount), the total cost of all socks is $144.
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Transportation: An app calculates that if a ride-sharing driver picks up 8 passengers, each contributing a fare based on a base fee of 9 dollars plus some variable amount \( x \), the total fare collected should be $144.
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Event Ticket Sales: For a fundraising event, tickets are sold where each ticket price includes a base fee of 9 dollars. If the organizers sell 8 tickets, they hope to raise a total of 144 dollars.
Each of these situations can be modeled by the equation \( 8(x + 9) = 144 \).
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