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astraxan [27]
2 years ago
6

Mr. Williams is building a sand box for his children. It costs $228 for the sand if he builds a rectangular-sand box with dimens

ions 9 ft by 6 ft. How much will the sand cost if he decides to increase the size to 1312 ft by 9 ft? A. $513 B. $289 C. $342 D. $380
Mathematics
2 answers:
Anvisha [2.4K]2 years ago
4 0

Answer:

A. $513

Step-by-step explanation:

Find the area of the boxes by multiplying the sides.

The first box is 54 ft sq.

The second box is 121.5 ft sq.

So

\\\frac{54}{121.5} =\frac{228}{x}

cross mult.

27702 = 54x

513 = x

Andru [333]2 years ago
3 0

Answer:  The correct option is (C) $342.

Step-by-step explanation:  Given that Mr. Williams is building a sand box for his children and is costs $228 for the sand if he builds a rectangular-sand box with dimensions 9 ft by 6 ft.

We are to find the cost of the sand if he decides to increase the size to 13\frac{1}{2}~\textup{ft by }9~\textup{ft}.

Since the box is empty from inside, so we will be considering the perimeter of the box, not area.

The perimeter of the rectangular-sand box with dimensions 9 ft by 6 ft is

P_1=2(9+6)=30~\textup{ft},

and the perimeter of the rectangular-sand box with dimensions 13\frac{1}{2}~\textup{ft by }9~\textup{ft}. is

P_2=2\left(13\dfrac{1}{2}\times9\right)=2(13.5\times9)=45~\textup{ft}.

Now, we will be using the UNITARY method.

Cost of sand for building rectangular-sand box with perimeter 30ft = $228.

So, cost of  sand for building rectangular-sand box with perimeter 1 ft will be

\$\dfrac{228}{30}.

Therefore, the cost of sand for building rectangular-sand box with perimeter 45 ft is given by

\$\dfrac{228}{30}\times45=\$342.

Thus, the required cost of the sand is $342.

Option (C) is CORRECT.

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When we factorise an expression, we are looking for simple factors that multiply to get the original expression. Usually it is very natural to factorise something like a quadratic in x. For example:

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This second example is closer to the question in hand. Just like x was a common factor to both x^2 and -9x, we are looking for a common factor to both 6b and 24bc. The common factor is 6b.

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3 0
2 years ago
Read 2 more answers
a cone with a radius 3 units is shown below. it’s volume is 57 cubic units. find the height of the cone
ipn [44]

<u>Given</u>:

Given that the radius of the cone is 3 units.

The volume of the cone is 57 cubic units.

We need to determine the height of the cone.

<u>Height of the cone:</u>

The height of the cone can be determined using the formula,

V=\frac{1}{3} \pi r^2 h

Substituting the values, r = 3 and V = 57, we get;

57=\frac{1}{3} (3.14) (3)^2 h

Simplifying the terms, we get;

57=\frac{1}{3} (3.14) (9) h

Multiplying both sides of the equation by 3, we get;

171= (3.14) (9) h

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8 0
3 years ago
One side of a rectangle is 9 millimeters shorter than six times the other side. Find the length of the longer side if we also kn
vodka [1.7K]

Given:

W(width) = (6L) - 9

L(length) = L

Equation:

2( [ 6L ] - 9) + 2 (L) = 150

= 12L - 18 + 2L = 150

= 12L + 2L = 150 + 18

=14L = 168

L = 168/14, so the length is 12. Let's check our work.

Width:  6(12) - 9 = 72 - 9 = 63

Length: 12

Since there are two lines of width and two lines of length:

2(12) + 2(63) = 24 + 126, which gives you a perimeter of 150 mm.

Hope this helped.

4 0
3 years ago
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