Problema Solution
You hire your friend John to help design your new kitchen. John is a creative designer but needs your help with the mathematics before he can get started.
The new kitchen is to be 20 feet long, and its width is 75% of its length. The door to enter the kitchen is on the short wall and is 10% of the width of that wall. You want to put in marble countertops, but you don’t want them to take up more than 1/20 of the space in your kitchen (space is in ft2). What is the largest area the counters can take up?
If your counters take up that much space and are 2 feet wide, how long are they?
You also want to tile your kitchen floor. If each tile is square and is 6 inches long, then how many tiles do you need for the whole floor? (Disregard allowance for grout, but don’t forget about the space the counters take up.)
Answer provided by our tutors
Let
l = 20 ft the length of the kitchen
w = the width of the kitchen, l>0
w = 0.75*l (its width is 75% of its length)
w = 0.75*20
w = 15 ft
The area of the kitchen A = length*width, that is:
A = 20*15
A = 300 ft^2
The counters can take up to 1/20 of the area in the kitchen or A1 = (1/20)*A = (1/20)*300 = 15 ft^2
The largest area the counters can take up is 15 ft^2.
If your counters take up that much space and are 2 feet wide, how long are they?
We will assume the counters are taking rectangular space.
Let
w1 = 2 ft the width of the counters
l1 = the length of the counters
A1 = 15 ft^2 the area of the counters
A1 = l1*w1
l1*2 = 15
........
........
l1 = 7.5 ft
The counters are 7.5 feet long.
The area of one tile is:
A2 = 6*6 (since the a squares with 6 inches long side)
A2 = 36 in^2
1 ft = 12 in
1 in = 1/12 ft
1 in^2 = (1/12)^2 ft^2
A2 = 36*(1/12)^2 ft^2
To find the number of tiles we divide (the total area - area of the counters)with the area per tile A2:
(A - A1)/A2 = (300 - 15)/(36*(1/12)^2) = 1,140 tiles
You need 1,140 tiles for the whole floor.