297: Systems of a Sort 3

A hotel rents a double-occupancy room for $30 more than a single-occupancy room. One night, the hotel took in $3115 after renting 15 double-occupancy rooms and 26 single-occupancy rooms. 

Other than by calling the hotel and asking directly, what ways could we use to find the single- and double- occupancy costs?

296: Systems of a Sort 2

What method works best to find the area of the triangle created by these three lines?
Organized list (a la excel)
Substitution?
Linear Combination?
Plug and Pray?

295: Systems of a Sort 1

In the following scenario, is there enough information to determine the cost of a bagel? Explain.

On Monday, the office staff at your school paid $8.75 for 4 cups of coffee and 7 bagels. On Wednesday, they paid $19.50 for 8 cups of coffee and 14 bagels. 

294: Equilateral Triangles and a square.

Equilateral triangles tile the plane. Is it possible to select four intersection points that are the corners of a perfect square?
— James Tanton (@jamestanton) October 18, 2014

293: Tight Fit

Seems as though this UHAUL truck got stuck.

Straightforward question: What's the diameter of that culvert?

Argument: What would have been a better way to phrase that sign so this wouldn't happen?

Dimensions

• Inside dimensions: 14'6" x 7'8" x 7'2" (LxWxH)
• Mom's Attic: 2'7" x 7'8" x 2'6" (LxWxH)
• Deck height: 2' 10"
• Door opening: 7'3" x 6'5" (WxH)
• Loading ramp width: 2'2"

292: What's This?

What is this?
What can we do with it?

Source.

291: Proof Without Words 7

What might all these kids be proving?

Source: Ed Southall (@edsouthall)