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30 May 2026, 10:59
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Formatted question: At a print shop, premium brochures cost $14 each and standard flyers cost $9 each. For an event, Nora ordered only premium brochures, and Eli ordered only standard flyers. How many premium brochures did Nora order?
(1) If Nora had ordered as many premium brochures as Eli ordered standard flyers, Nora’s order would have cost $45 more than Eli’s order.
(2) If Nora had ordered standard flyers instead, in the same quantity as the premium brochures she actually ordered, her total cost would have been $35 less.
(1) If Nora had ordered as many premium brochures as Eli ordered standard flyers, Nora’s order would have cost $45 more than Eli’s order.
(2) If Nora had ordered standard flyers instead, in the same quantity as the premium brochures she actually ordered, her total cost would have been $35 less.
30 May 2026, 10:59
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Official Solution:
At a print shop, premium brochures cost $14 each and standard flyers cost $9 each. For an event, Nora ordered only premium brochures, and Eli ordered only standard flyers. How many premium brochures did Nora order?
Let \(p\) be the number of premium brochures Nora ordered, and let \(s\) be the number of standard flyers Eli ordered.
Then Nora’s total cost was \(14p\) dollars, and Eli’s total cost was \(9s\) dollars.
(1) If Nora had ordered as many premium brochures as Eli ordered standard flyers, Nora’s order would have cost $45 more than Eli’s order.
If Nora had ordered as many premium brochures as Eli ordered standard flyers, then that hypothetical order would have cost \(14s\) dollars, while Eli’s actual order cost \(9s\) dollars.
So (1) gives:
\(14s - 9s = 45\)
\(s = 9\)
This determines only how many standard flyers Eli ordered. It does not determine \(p\). Not sufficient.
(2) If Nora had ordered standard flyers instead, in the same quantity as the premium brochures she actually ordered, her total cost would have been $35 less.
If Nora had ordered standard flyers instead, in the same quantity, then her cost would have been \(9p\) dollars instead of \(14p\) dollars.
So (2) gives:
\(14p - 9p = 35\)
\(p = 7\)
This determines the number of premium brochures Nora ordered. Sufficient.
Answer: B
At a print shop, premium brochures cost $14 each and standard flyers cost $9 each. For an event, Nora ordered only premium brochures, and Eli ordered only standard flyers. How many premium brochures did Nora order?
Let \(p\) be the number of premium brochures Nora ordered, and let \(s\) be the number of standard flyers Eli ordered.
Then Nora’s total cost was \(14p\) dollars, and Eli’s total cost was \(9s\) dollars.
(1) If Nora had ordered as many premium brochures as Eli ordered standard flyers, Nora’s order would have cost $45 more than Eli’s order.
If Nora had ordered as many premium brochures as Eli ordered standard flyers, then that hypothetical order would have cost \(14s\) dollars, while Eli’s actual order cost \(9s\) dollars.
So (1) gives:
\(14s - 9s = 45\)
\(s = 9\)
This determines only how many standard flyers Eli ordered. It does not determine \(p\). Not sufficient.
(2) If Nora had ordered standard flyers instead, in the same quantity as the premium brochures she actually ordered, her total cost would have been $35 less.
If Nora had ordered standard flyers instead, in the same quantity, then her cost would have been \(9p\) dollars instead of \(14p\) dollars.
So (2) gives:
\(14p - 9p = 35\)
\(p = 7\)
This determines the number of premium brochures Nora ordered. Sufficient.
Answer: B
