Isaiah And Cooper work at a dry cleaner Ironing shirts.isaiah can iron 25 shirts per hour, and Cooper can iron 30 shirts per hou
r. Cooper worked twice as many hours as Isaiah And they ironed 340 shirts between them. Write a system of equations that could be used to determine the number of hours Isaiah worked and the number of hours cooper worked . Define the variables that you use to write the system
2 answers:
<u>Define Variables:</u>
Let x = the number of hours Isaiah worked
Let y = the number of hours Cooper worked
Isaiah can iron 25 shirts each hour, so in x hours he can iron 25x shirts. Cooper can iron 30 shirts each hour, so in y hours he can iron 30y shirts. The total number of shirts ironed 25x+30y equals 340
Since Cooper worked twice as many hours as Isaiah, Cooper worked <em>more </em>hours, so if we multiply 2 by the number of hours Isaiah worked, we will get the number of hours Cooper worked, meaning y equals 2x.
<u>System of Equations:</u>
25x + 30y = 340
y = 2x
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Answer:
Part 1: 31.4 feet
Part 2: 61 feet
Part 3: 99,000 stalks of corn
Step-by-step explanation:
<u>Part 1:</u>
Diagram attached.
You can follow the problem closely and draw a diagram like this. The RED LINE is the distance we are looking to find.
The red line is the hypotenuse of a right triangle we can create (see the dotted line). We can now use the pythagorean theorem to solve for the distance.
Pythagorean Theorem is hypotenuse^2 = leg^2 + leg^2
Let red line [what we want to find] be h and the other 2 sides are 10-5=5 ft & 25 + 6 = 31ft. So we have:
Hence Bethany has to walk 31.4 feet
<u>Part 2:</u>
See 2nd diagram attached.
The blue line is the path of Bethany and the green line is path of Ben. The RED line is what we are looking to find, the shortest distance between them.
We use Pythagorean Theorem twice on the two triangles and add up the results.
<u>Left Triangle:</u>
If we make a triangle, we have base (one leg) = 30 and the other leg is 20-10=10. So we have:
<u>RightSide triangle:</u>
two legs are 25 and 15 respectively, so we use the pythagorean theorem again:
Thus, the shortest distance = 31.62 + 29.15 = 60.77 = 61 feet (rounded to nearest whole number)
<u>Part 3:</u>
The area of the Maize MINUS the area of the path is the Area of the Corn [what we are looking for].
Area of Maze:
100 * 100 = 10,000 sq. yd.
Area of Path = 1.5 * 3000 = 4,500 sq. yd.
Area of Corn = 10,000 - 4,500 = 5,500 sq. yard of land.
Now, each sq. yd. holds 18 stalks, so 5,500 sq. yd. will hold:
18 * 5,500 = 99,000 stalks of corn
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