MATHEMATICS HIGH SCHOOL

There are some books on three shelves. On the bottom shelf there are half as many books as on the other two shelves. On the middle shelf there are three times less than on the other two shelves. On the top shelf there are 30 books. How many books are on all three shelves?

Answers

Answer 1

Answer:

Answer:

There are 72 books on all the three shelves.

Step-by-step explanation:

Given:

On the bottom shelf there are half as many books as on the other two shelves.

On the middle shelf there are three times less than on the other two shelves.

On the top shelf there are 30 books.

Now, to find the books on all three shelves.

Let the books on the middle shelf be $x.$

The books on the top shelf are 30.

The books on the bottom shelf = $(1)/(2) (x+30)$

So, the books on the middle shelf:

$3x=30+(1)/(2)(x+30)$

$3x=30+(x+30)/(2)$

$3x=(60+x+30)/(2)$

Multiplying both sides by 2 we get:

$6x=60+x+30$

$6x=x+90$

Subtracting both sides by $x$ we get:

$5x=90$

Dividing both sides by 5 we get:

$x=18.$

Thus, the books on middle shelf are 18.

Now, to get the books on the bottom shelf by substituting the value of $x$ :

$(1)/(2) (x+30)$

$=(1)/(2) (18+30)\n\n=(1)/(2) * 48\n\n=24.$

Hence, the books on the bottom shelf are 24.

Now, to get the total books on all the three shelves we add the books of top, middle and bottom shelf:

$30+18+24\n\n=72.$

Therefore, there are 72 books on all the three shelves.

Related Questions

The entire exterior of a large wooden cube is painted red, and then the cube is sliced into n^3 smaller cubes (where n > 2). Each of the smaller cubes is identical. In terms of n, how many of these smaller cubes have been painted red on at least one of their faces?A. 6n^2B. 6n^2 – 12n + 8C. 6n^2 – 16n + 24D. 4n^2E. 24n – 24
Suppose customers in a hardware store are willing to buy N(p) boxes of nails at p dollars per box, as given by the following function.N(P) = 80 - 4p^2 ; 1 <= p <= 4. Find the average rate of change in the number of boxes of nails that customers are willing to buy (demand) for a change in price from $2 to $3.The average rate of change of demand for a change in price from $2 to $3 is ___ boxes per dollar.(Type an integer or a decimal.)I know the answer (-20) but I am not sure how to get it. Can you help?
Jean Marie has $4,000 in the bank, $500 worth of credit card debt and a $15,000 student loan. Jean Marie would like to know her net worth. She finds the difference between her assets, $4,500, and her liabilities, $15,000, and determines her net worth is -$10,500. Evaluate Jean Marie's determination.- Her calculations are correct. - She counted a liability as an asset. - She counted an asset at a liability. - Her answer should be positive.
If b = 1/2x −1/y, then what is an expression for 2/b in terms of x and y?
Brian drives a distance of 250 m at a speed of 50 m/sec. With what speed should hedrive so that he covers twice the distance in the same time?2 Marks

A 40-foot T.V. antenna stands on top of a building. From a point on the ground, the angle of elevation to the top and to the bottom of the antenna measures 56° and 42° respectively. How tall is the building?

Answers

Answer:

61.5

Step-by-step explanation:

In this case to calculate the height, we do the following:

The first is the graphic, attached image.

Then the calculations.

b / d = tan (42 °) = 0.9

d = b / 0.9

Then we have to:

(40 + b) / d = tan (56 °) = 1.48

(40 + b) = d * 1.48

Replacing we have:

(40 + b) = (b / 0.9) * 1.48

40 + b = 1.65 * b

1.65 * b - b = 40

b = 40 / 0.65

b = 61.5

Therefore the height is approximately 61.5

Final answer:

Using the tangent function of trigonometry for the two given angles, we can set up two equations. We solve these equations by substituting the fabricate distance from one into the other, providing the height of the building.

Explanation:

To find the height of the building, we'll use the tangent function of trigonometry. In this case, the tangent of an angle in a right triangle is defined as the opposite side divided by the adjacent side. Therefore, we create two equations using the two provided angles and the respective opposite sides (antenna and building + antenna), as we know the distances are proportional to the tangent of their angles when the adjacent side (distance from the point on the ground to the building) is the same.

For the entire structure (building + antenna): tan(56 degrees) = (Height of building + 40 feet) / Distance from the building.
For the antenna only: tan(42 degrees) = 40 feet / Distance from the building.

We can solve this system of equations by substitution. Since tan(42 degrees) = 40 feet / Distance from the building, it means the Distance from the building = 40 feet / tan(42 degrees). Plugging the Distance into equation 1 and solving for Height of building, we get: Height of building = tan(56 degrees) * Distance from building - 40 feet = tan(56 degrees) * (40 feet / tan(42 degrees)) - 40 feet. This gives us the height of the building.

Learn more about Trigonometry here:

brainly.com/question/11016599

#SPJ11

2x -y=-1
3x-2y=1
elimination somebody do this for me

Answers

2x-y=-1 (1)
3x-2y=1 (2)
(1) * 2--> 4x-2y=-2 (3)
(3) - (2)
x= -3

sub x= -3 into (1)
2(-3)-y=-1
-6-y=-1
-y=5
y= -5

-2(2x-y)=-1
3x-2y=1

-4x+2y=2
3x-2y=1

-x=3 (x=-3)
(-3,__)

2(-3)-y=-1
-6-y=-1
-y=-1+6
-y=5
y=-5
so..(-3,-5)

A computer company uses the function f(h) = 50h + 75 to calculate the total repair bill, f(h), for h number of hours worked. Find h if f(h) = $275. 13,825 hours
13,750 hours
4 hours
2 hours

Answers

4 Hours because 50 times 4 is 200 and 200+75 is 275

4 hours is the answer to your question.

your order comes in for new protective eye wear. you order five and a half dozen. how many individual protective eye wear should you have recieved

Answers

You should have received 33 pairs of protective eyewear

To Check This:
1 dozen = 12
1/2 dozen = 6
5 dozen = 60

12x5=60+6=66
66 / 2 = 33 because a pair equals 2

For the first 500 minutes used each month, the customer is charged a flat rate of $50. These 500 minutes are "included" in their monthly plan.For any additional minutes used, the customer is charged an additional $.10 per minute.
Is it linear