Subjects algebra

Pizza Delivery 3Fd567

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1. **State the problem:** A restaurant charges a delivery fee plus the price of pizzas. One customer pays 25 for 2 pizzas, another pays 58 for 5 pizzas. Find how many pizzas a customer gets for 80. 2. **Set variables:** Let $d$ be the delivery fee and $p$ be the price per pizza. 3. **Write equations from given data:** For 2 pizzas: $$d + 2p = 25$$ For 5 pizzas: $$d + 5p = 58$$ 4. **Subtract first equation from second to eliminate $d$:** $$ (d + 5p) - (d + 2p) = 58 - 25 $$ $$ \cancel{d} + 5p - \cancel{d} - 2p = 33 $$ $$ 3p = 33 $$ 5. **Solve for $p$:** $$ p = \frac{33}{3} = 11 $$ 6. **Substitute $p=11$ into first equation to find $d$:** $$ d + 2(11) = 25 $$ $$ d + 22 = 25 $$ $$ d = 25 - 22 = 3 $$ 7. **Write total cost formula:** $$ \text{Total cost} = d + p \times \text{number of pizzas} = 3 + 11x $$ 8. **Find number of pizzas $x$ for total cost 80:** $$ 3 + 11x = 80 $$ $$ 11x = 80 - 3 = 77 $$ $$ x = \frac{77}{11} = 7 $$ **Answer:** A customer who pays 80 receives 7 pizzas.