John wants to plan a big party for his parents' 25th anniversary. Jill's Catering charges $100 to rent their building and $30 per dinner. El Sombrero charges $150 to rent their facility and $25 per plate. For how many guests will the cost be in the same at the two caterers?

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John wants to plan a big party for his parents' 25th anniversary. Jill's Catering charges $100 to rent their building and $30 per dinner. El Sombrero charges $150 to rent their facility and $25 per plate. For how many guests will the cost be in the same at the two caterers?

Mathematics
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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The sum is the same and is presented like this: S = initialFee + guests * costPerGuest S(Jill) = 100 + 30x S(Sombrero) = 150 + 25x 100 + 30x = 150 + 25x 5x = 50 x = 10 Test drive: 10 guests at Jill's will cost 100 + 30 * 10 = 400 10 guests at the Sombrero will cost 150 + 25 * 10 = 400
After that Sombrero is cheaper of course, 11 guests at Jill's for 430 vs Sombrero's 425.
And for <=9 Jill's was cheaper.

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