Which fractions equal the whole number 3?
2 answers:
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Answer:
150 quartz of creamy vanilla and 50 quartz of Continental Mocha.
Step-by-step explanation:
Let x represents the number of quartz of Creamy vanilla and y represents the number of Continental Mocha,
∵ There is a profit of $ 3 on each quart of Creamy Vanilla and $2 on each quart of Continental Mocha.
So, the total profit,
Z = 3x + 2y
Which is the objective function for this problem that has to maximise,
Each quart of Creamy Vanilla go 2 eggs and 3 cups of cream,
So, in creamy vanilla,
Number of eggs = 2x
Cups of cream = 3x
Also, Each quart of Continental Mocha go 1 egg and 3 cups of cream,
So, in creamy vanilla,
Number of eggs = y
Cups of cream = 3y
Thus, total number of eggs = 2x + y
And, total number of cups of cream = 3x + 3y
According to the question,
2x + y ≤ 350
3x + 3y ≤ 600
Which are subject of constraint,
Graphing :
Related equation of 2x + y ≤ 350 is 2x + y = 350,
Having x-intercept = (175,0) y-intercept = (0, 350)
Also, 2(0) + 0 ≤ 350 ( True )
∴ Shaded region of 2x + y ≤ 350 would contain the origin,
Related equation of 3x + 3y ≤ 600 is 3x + 3y = 600,
Having x-intercept = (200,0) y-intercept = (0, 200)
Also, 3(0) + 3(0) ≤ 600 ( True )
∴ Shaded region of 3x + 3y ≤ 600 would contain the origin,
'≤' shows solid line,
By graphing them we obtain a feasible region,
In which boundary points are (0, 200), (150, 50) and (175,0)
At (0, 200),
Z = 3(0) + 2(200) = $ 400,
At ( 150, 50)
Z = 3(150) + 2(50) = 450 + 100 = $ 550
At ( 175, 0)
Z = 3(175) + 2(0) = $ 525
Hence, 150 quartz of creamy vanilla and 50 quartz of Continental Mocha should make to earn the largest profit.
To find the length of side of square, we have to use distance formula.
Points are (-4,-6) and (5,-1)
Formula for distance between two points.
So length of side of square is 10.3 units.
Answer: 10.3 units
Points are (-4,-6) and (5,-1)
Formula for distance between two points.
So length of side of square is 10.3 units.
Answer: 10.3 units