Which is the best first step when solving the following system of equations?
1 answer:
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Part I: Scale Drawing
<span>Decide on a scale factor to represent the distance covered by the patio. Then, use the space below to design Mrs. Johnson’s patio to be a square that is at least 8 feet on each side.</span>
a) Scale Factor: 1 in/ 2 ft
Use a straightedge and a ruler to draw to scale a design for Mrs. Johnson’s patiob) see the picture attached
Mrs. Johnson’s patio to be a square that is 10 ft x 10 ft
<span><span>c) What are the dimensions of Mrs. Johnson’s patio? </span>
</span>the dimensions of Mrs. Johnson’s patio are 10 ft x 10 ft
<span><span>d) Calculate the area of Mrs. Johnson’s patio. Show all work.
</span> </span>
area of the square=b²
where b is the length side of the square
b=10 ft
so
Area=10²-----> area =100 ft²
<span><span>e) How many pavers will be needed? Show all work. </span>
</span>
we know that
1 paver is 16 in x 16 in dimensions
convert to ft
1 ft----------->12 in
x ft-----------> 16 in
x=16/12-----> x=4/3 ft
so
1 paver is (4/3) ft x (4/3) ft dimensions
area of one paver=(4/3)²----> 16/9 ft²
if one paver has an area of----------------> 16/9 ft²
x pavers-----------------------> 100 ft²
x=100/(16/9)------> x=100*9/16-----> x=56.25 pavers
if one box --------------> 12 pavers
x box---------> 56.25 pavers
x=56.25/12-----> x=4.68 box-------> x=5 boxes
5 boxes of pavers will be needed
<span><span>f) What will it cost to build the patio? Show all work.
</span> </span>
the cost of one box is--------> $99.99
5 boxes-----------> x
x=5*$99.99------>x=$499.95
the cost to build the patio is $499.95
Part II: Bigger Design
<span>There is a saying that bigger is better, so why not double the dimensions of Mrs. Johnson’s patio to make the side measurement twice as big? Mrs. Johnson and I think that it would better meet her needs. After seeing the original estimation, she thinks that she could afford to double the size. I explained that making the patio twice as big would mean twice the cost. Mrs. Johnson says, “Let’s do it!”</span>
<span>a) What would be the new dimensions of Mrs. Johnson’s patio?
</span>the new dimensions of Mrs. Johnson’s patio are 20 ft x 20 ft
<span>b) Calculate the new area of Mrs. Johnson’s patio. Show all work.
</span>area of the square=b²
where b is the length side of the square
b=20 ft
so
Area=20²-----> area =400 ft²<span>
</span>
<span><span>c) How many pavers will be needed for the new design? Show all work.
</span> </span>
1 paver is (4/3) ft x (4/3) ft dimensions
area of one paver=(4/3)²----> 16/9 ft²
if one paver has an area of----------------> 16/9 ft²
x pavers-----------------------> 400 ft²
x=400/(16/9)------> x=400*9/16-----> x=225 pavers
if one box --------------> 12 pavers
x box---------> 225 pavers
x=225/12-----> x=18.75 box-------> x=19 boxes
19 boxes of pavers will be needed
<span>d) What will it cost to build the bigger patio? Show all work.
</span>the cost of one box is--------> $99.99
19 boxes-----------> x
x=19*$99.99------>x=$1899.81
the cost to build the bigger patio is $1899.81
<span><span>e) Is Khianna right? Will doubling the size of the patio, double the cost?</span>
</span>
<span>Khianna is wrong to double the dimensions the cost quadruples</span>
