I really need help with this

Mike and Ken shared some stamps. \frac{1}{5} 5 1 of Ken's stamps were \frac{1}{3} 3 1 of Mike's stamps. If Mike gave Ken 24

Zielflug [23.3K]

Answer:

Mike had 72 stamps

Ken had 120 stamps

Step-by-step explanation:

Given

$M \to Mike$

$K \to Ken$

$\frac{1}{5} * K = \frac{1}{3} * M$

$K + 24 = 3 * ( M - 24)$

Required

Find K and M

Make K the subject in: $K + 24 = 3 * ( M - 24)$

$K = 3 * ( M - 24) - 24$

Substitute $K = 3 * ( M - 24) - 24$ in $\frac{1}{5} * K = \frac{1}{3} * M$

$\frac{1}{5} * [3 * ( M - 24) - 24] = \frac{1}{3} * M$

Open brackets

$\frac{1}{5} * [3M - 72 - 24] = \frac{1}{3} * M$

$\frac{1}{5} * [3M -96] = \frac{1}{3} * M$

Multiply both sides by 15

$3* [3M -96] = 5 * M$

$9M -288 = 5M$

Collect like terms

$9M -5M= 288$

$4M= 288$

Divide both sides by 4

$M= 72$

Substitute $M= 72$ in $K = 3 * ( M - 24) - 24$

$K = 3 * (72 - 24) - 24$

$K = 3 * 48 - 24$

$K = 120$

3 0

3 years ago

Is the answer 200? Or 4.5??? Or is none ? I don't know it's confusing :/ can I get help :/

skelet666 [1.2K]

Let x = the number of penguins we are finding

x ÷ 100 × 30 = 15
x = 15 ÷ 30 × 100
x = 50

hope this helps and have a great day :)

6 0

3 years ago

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Find the product. (y^2)^5 · y^8 y^23 y^18 (y)^40 y^1/5

Klio2033 [76]

This question requires you to solve,

(y²)⁵×y⁸ =y⁽²ˣ⁵⁾ × y⁸
= y¹⁰ × y⁸
= y⁽¹⁰⁺⁸⁾
= y¹⁸
The correct answer is y¹⁸

4 0

3 years ago

It takes 154 cubes with side lengths of 1/2 inch to fill a rectangular prism. What is the volume of the rectangular prism? Show

Tju [1.3M]

Answer:

The volume of the rectangular prism is 19.25 inches³.

Step-by-step explanation:

Given:

It takes 154 cubes with side lengths of 1/2 inch to fill a rectangular prism.

Now, to find the rectangular prism's volume.

We first find the volume of a cube to fill in the rectangular prism.

The side length of the cube = $\frac{1}{2}\ inch.$

Now, to get the volume of cube we put formula:

$Volume=(side)^3\\\\Volume=(\frac{1}{2})^3 \\\\Volume=\frac{1}{8}\ inch^3.$

Thus, the volume of a cube is $\frac{1}{8} \ inch^3.$

Number of cubes = 154.

According to question, it takes 154 cubes to fill the rectangular prism.

So, to get the volume of prism we need to find the volume of 154 cubes.

Now, to get the volume of 154 such cubes we multiply the volume of a cube by number of cubes:

$\frac{1}{8}\times 154\\\\ =\frac{154}{8}\\\\ =19.25\ inches^3.$

Therefore, the volume of the rectangular prism is 19.25 inches³.

3 0

3 years ago

There are 24 men and 36 women in a choir.

Molodets [167]

Answer:

Step-by-step explanation:

Total members in the choir = 24 + 36 = 60

a) Percentage of men = $\frac{24}{60}*100$

= 4 * 10 = 40%

b) Percentage of women = 60%

c) Number of men =24 + 10 = 34 men

Number of women = 36 + 10 = 46

Total = 34 + 46 = 80

Percentage of men = $\frac{34}{80}*100= 42.5$ %

Percentage of women = (100 - 42.5)% = 57.5%

6 0

3 years ago

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