Subjects algebra

Profit Expression Fdfad2

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1. **State the problem:** TechWiz Electronics makes a profit of 35 for each MP3 player sold and 136 for each DVD player sold. Last week, they sold a combined total of MP3 and DVD players. Let $x$ be the number of MP3 players sold last week. 2. **Define variables:** Let $x$ = number of MP3 players sold. Let $y$ = number of DVD players sold. 3. **Write the total number of players sold:** Since the total number of MP3 and DVD players sold is a combined total, we have: $$x + y = \text{total number sold}$$ 4. **Express $y$ in terms of $x$:** $$y = \text{total number sold} - x$$ 5. **Write the profit expression:** Profit from MP3 players = $35x$ Profit from DVD players = $136y$ 6. **Substitute $y$ into profit expression:** $$\text{Total profit} = 35x + 136(\text{total number sold} - x)$$ 7. **Simplify the expression:** $$\text{Total profit} = 35x + 136 \times \text{total number sold} - 136x$$ $$= (35x - 136x) + 136 \times \text{total number sold}$$ $$= -101x + 136 \times \text{total number sold}$$ **Final expression:** $$\boxed{\text{Total profit} = 136 \times \text{total number sold} - 101x}$$ This expression gives the combined total profit in terms of $x$, the number of MP3 players sold, and the total number of players sold.