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charle [14.2K]
3 years ago
15

There are 900 toothpicks in a​ regular-sized box. If a jumbo box is made by tripling all the dimensions of the​ regular-sized bo

x, how many toothpicks will the jumbo box​ hold?
Mathematics
2 answers:
Colt1911 [192]3 years ago
6 0

When you triple the height of the box, it can hold (900 x 3) = 2,700 pieces.

Then triple its length, and it can hold (2,700 x 3) = 8,100 pieces.

Then triple its width, and it can hold (8,100 x 3) = 24,300 pieces.

When you triple the dimensions of a 3D object, it has 27 times its original volume.  (900 x 27) = 24,300 .

Vaselesa [24]3 years ago
4 0

Answer: 24300 toothpicks

Step-by-step explanation:

The volume of the box can be written as:

V0 = W*L*H

where W is the width, L is the length and H is the height.

We know that in V0 we can put 900 toothpicks.

Now, if we triply each of the dimensions we have that:

V = 3W*3L*3H = (3*3*3)*W*L*H

and we know that W*L*H = V0

V = 27*V0

and if in V0 we can put 900 toothpicks, then in V we can put 27 times that amount, this is:

27*900 = 24300 toothpicks

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A sweet factory produces 5 different chocolate bars. the different flavors are always produced in the same proportions, for ever
IRISSAK [1]

a. There are 933 chocolate bars

b. There are 1200 chocolate bars

c. There are 1580 chocolate bars

<h3>How to calculate the number of chocolate bars</h3>

Since there are 5 different flavors,

let

  • x = orange flavored bars,
  • y = coconut flavored bars,
  • z = coffee flavored bars,
  • a = strawberry flavored bars and
  • b = honeycomb flavored bars and
  • X = total number of bars

Since the different flavors are always produced in the same proportions, for every 4 coconut flavored bars 5 honeycomb 6 orange 1 coffee and 4 strawberry

So, the ratio of their proportions are x:y:z:a:b = 6:4:2:1:5

So, the total ratio is T = 6 + 4 + 1 + 4 + 5 = 20

<h3>a. What is the total number of chocolate bars if there are 280 orange flavored bars?</h3>

Since we have 6 orange flavored bars, the ratio of orange flavored bars to total is 6/20

So, the amount of orange flavored bars is x = 6/20 × X

Making X subject of the formula, we have

X = 20x/6

So, if there are 280 orange bars, there will be

X = 20x/6

X = 20 × 280/6

X = 5600/6

X = 933.33

X ≅ 933 chocolate bars

So, there are 933 chocolate bars

<h3>b. What is the total number of chocolate bars if there are 960 coconut flavored bars?</h3>

Since we have 4 coconut flavored bars, the ratio of coconut flavored bars to total is 4/20

So, the amount of coconut flavored bars is y = 4/20 × X

Making X subject of the formula, we have

X = 20y/4

So, if there are 960 coconut flavored bars, there will be

X = 20y/6

X = 20 × 960/4

X = 5 × 240

X = 1200 chocolate bars

So, there are 1200 chocolate bars

<h3>c. What is the total number of chocolate bars if there are 79 coffee flavored bars?</h3>

Since we have 1 coffee flavored bars, the ratio of coffee flavored bars to total is 1/20

So, the amount of coconut flavored bars is z = 1/20 × X

Making X subject of the formula, we have

X = 20z

So, if there are 79 coffee flavored bars, there will be

X = 20z

X = 20 × 79

X = 1580 chocolate bars

So, there are 1580 chocolate bars

Learn more about ratio here:

brainly.com/question/1127546

#SPJ1

7 0
1 year ago
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