Answer: The original number is 175
Step-by-step explanation:
The number will be represent by x .
The number is being divided by 5 so we can represent by the expression x/5.
After than is being added to 18 so we will add 18 to the expression.
x/5 + 18 .
It has to equal to 9 less than 62 and 9 less than 62 is the same as the expression 62 -9.
Whole equation will be x/5 + 18 = 62 - 9
+ 18 = 62 - 9 Combine like terms on the right side
x/5 + 18 = 53 Subtract 18 from both sides
-18 -18
x/5 = 35 Multiply both side by 5.
x = 175
This means the original number is 175.
Answer:
x=2
Step-by-step explanation:
Here what we need is that the ratios be equal, which is:
x:(5/2) = 8:10 or, what is the same:
x/(5/2) = 8/10
Lets pick the left term x/(5/2) and multiply both numerator and denominator by 2 to eliminate the fraction on the denominator:
2x/2(5/2) = 2x/5
Now, we would like to make a 10 appear on the denominator. As we already have a five we need to multiply numerator and denominator by the num that, multiplied by 5 gives as 10, this is 2:
2(2x)/2(5) = 4x / 10
So, we transformed x/(5/2) in 4x/10, and both are the same, so we can replace it on our first equation:
4x/10 = 8/10
As both denominators are equal, we can concentrate only in numerators:
4x = 8
Dividing both sides by 4:
x = 2
So, for x=2 both ratios are equivalents.
Answer:
its 24 hope this helps
Step-by-step explanation:
The amounts of sugar, butter, and flour used are 150 grams, 225 grams, and 450 grams, respectively.
Anders makes scones with three ingredients : sugar, butter, and flour. The ratio of the amounts of sugar, butter, and flour is 2:3:6. The available amounts of the ingredients in the kitchen include 200 grams of sugar, 300 grams of butter, and 450 grams of flour. He makes as many scones as he can with these ingredients.
Let the amounts of sugar, butter, and flour be 2x, 3x, and 6x, respectively. The maximum proportion is for flour. The amount of flour used is 450 grams. The amount of butter used is half of that of the flour. The amount of sugar is one-third of that of flour.
B = (3x/6x)*450 = 225
S = (2x/6x)*450 = 150
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The largest possible volume of the given box is; 96.28 ft³
<h3>How to maximize volume of a box?</h3>
Let b be the length and the width of the base (length and width are the same since the base is square).
Let h be the height of the box.
The surface area of the box is;
S = b² + 4bh
We are given S = 100 ft². Thus;
b² + 4bh = 100
h = (100 - b²)/4b
Volume of the box in terms of b will be;
V(b) = b²h = b² * (100 - b²)/4b
V(b) = 25b - b³/4
The volume is maximum when dV/db = 0. Thus;
dV/db = 25 - 3b²/4
25 - 3b²/4 = 0
√(100/3) = b
b = 5.77 ft
Thus;
h = (100 - (√(100/3)²)/4(5.77)
h = 2.8885 ft
Thus;
Largest volume = [√(100/3)]² * 2.8885
Largest Volume = 96.28 ft³
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