A construction worker is building a wall. The wall is 17.5 yds long. He needs to place a stud every 15 inches. The first stud ha
s already been placed at one end of the wall. How many additional studs are needed, if the last stud will be placed at the other end of the wall? First fill in the blanks on the left side using the ratios shown. Then write your answer.
1 answer:
The correct answers are:
Box-1:
Box-2:
Box-3:
Box-4: <em>42</em> studs
Explanation:
Given:
Wall is 17.5 yds long.
<em>In 1 yard, there are 3 feet.</em>
Therefore,
In Box-1, you should put .
<em>In 1 foot, there are 12 inches.</em>
Therefore,
In Box-2, you should put .
<em>He needs to place 1 stud every 15 inches.</em>
Therefore,
In Box-3, you should put .
<em>Now multiple all the numbers, you will get the number of studs.</em>
<em></em>
In Box-4, write 42 studs.
-i
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c: number of color copies
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</span><span>3c + b
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</span><span>ii) He needs to print at least 6 copies ⇒ c + b ≥ 6
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2) Name the variables.
c: number of color copies
b: number of black-and-white copies
3) Model each restriction:
i) <span>It takes 3 minutes to print a color copy and 1 minute to print a black-and-white copy.
</span><span>
</span><span>3c + b
</span><span>
</span><span>
</span><span>ii) He needs to print at least 6 copies ⇒ c + b ≥ 6
</span><span>
</span><span>
</span><span>iv) And must have the copies completed in no more than 12 minutes ⇒</span>
3c + b ≤ 12
<span />
4) Additional restrictions are c ≥ 0, and b ≥ 0 (i.e. only positive values for the number of each kind of copies are acceptable)
5) This is how you graph that:
i) 3c + b ≤ 12: draw the line 3c + b = 12 and shade the region up and to the right of the line.
ii) c + b ≥ 6: draw the line c + b = 6 and shade the region down and to the left of the line.
iii) since c ≥ 0 and b ≥ 0, the region is in the first quadrant.
iv) The final region is the intersection of the above mentioned shaded regions.
v) You can see such graph in the attached figure.