FC: Tapestry Word Problem (#25) | Paul Lapre
1: Question 25: You are on the decorating committee for your school, and the committee has decided to hang a beautiful tapestry on the front of the main building, honoring the school's new music program. You've been entrusted with the task of finding the material to border it! The tapestry right now is 5 feet tall and 7 feet wide. You found some beautiful glittery material for a big border to go around the entire thing, and you found these great 1-foot-tall music notes to put on the border! But this special material is expensive, and due to budget constraints, you're only allowed to buy 45 square feet of it. -Write the length and width of the border as functions of x. What kind of functions are these? -Write the area of the border as a funtion of x. What kind of function is this? -If the border has a uniform thickness all the way around, what is the maximum thickness for the border? -Will the music notes fit on the border? Explain.
2: Write the length and width as functions of x. Length: f(x)=2x+7 Width: f(x)=2x+5 The functions for length and width are linear functions, and binomials.
3: Write the area of the border as a function of x Area: f(x)=4x^2+24x The function representing the area of the border is a quadratic function.
4: If the border has a uniform thickness all the way around, what is the maximum thickness for the border? -The maximum thickness for the border is 1.5 feet.
5: Will the music notes fit on the border? Explain. -Yes, the notes will fit on the border because the border, as said in the previous page, can be 1.5' tall and wide, which will easily accommodate for the 1' tall music notes.