Peter sells cards in packs of 12 and envelopes in packs of 27. If Martha wants the same number of each, what is the minimum number of cards that she will have to buy?

Answers

Answer 1
Answer: The lowest common multiple of 12 and 27 is 108.

12 x 9 = 108  and 
27 x 4 = 108 .

So she has to buy 9 packs of cards ... 108 of them ... and 4 packs of envelopes.


Answer 2
Answer: she will need to buy at least three hundred and twenty four cards (324) cards.

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The concert lasts 60 minutes, and the songs are all the same length. The choir sings a total of 12 songs, 2 of which are sung by the sopranos only. For how many minutes do the sopranos sing by themselves? Solve the equations using a letter for the unknown quantity.

Answers

60mins= 12x
60/12=12x/12
5=x
x= length of songs
5 x 2= 10 mins soprano sings by themselves

Answer:

10 minutes

Step-by-step explanation:

60 / 12 = 5

5 *2 = x=10

this means that x = 10

Write the equation and solve it. Melanie had 345 dollars to spend on 9 books. After
buying them she had 12 dollars. How much did each book cost ?
Someone help

Answers

Equation: 9x + 12 = 345
Answer: 37

Answer: 345 - 9x = 12 is the equation. Each book cost $37.

Step-by-step explanation: 345 - 12 = 333. This reveals that she spent $333 on books. We divide this by nine to find how much each cost. 333 / 9 = 37. In the equation, x = 37.

a park is shaped like a rectangle with a length 5 miles it's width w. what is a simplified expression for the distance between opposite corners of the park?

Answers

Let the distance between the two corners be AB.

Now, according to the pythagoras theorum,

AB² = 5² + w²

Thus, AB  = √25+w²

Thus, the distance between the two corners is √25+w² 

Katherine has $140 in the bank and is saving $6 per week. Abbie has $462 in the bank, but is spending at a rate of $10 per week. Which equation will determine when they will have the same amount of money in the bank?

Answers

Katherine=140+6x
Abbie= 462-10x

Answer:

thank you

Step-by-step explanation:

A dog weighs two pounds less than three times the weight of a cat. The dog also weighs twenty-two pounds more than a cat. Write and solve an equation to find the weights of the dog and the cat.

Answers

Let's use algebra to represent the weights of the dog and the cat.

Let D represent the weight of the dog in pounds.

Let C represent the weight of the cat in pounds.

According to the information given:

1. The dog weighs two pounds less than three times the weight of a cat, so we can write this as an equation: D = 3C - 2.

2. The dog also weighs twenty-two pounds more than a cat, so we can write this as another equation: D = C + 22.

Now, we have a system of two equations:

1. D = 3C - 2

2. D = C + 22

To solve for the weights of the dog and the cat, we can set these two equations equal to each other since they both equal D:

3C - 2 = C + 22

Now, let's solve for C (the weight of the cat):

3C - C = 22 + 2

This simplifies to:

2C = 24

Now, divide both sides by 2 to find the value of C (the weight of the cat):

C = 24 / 2

C = 12

So, the weight of the cat is 12 pounds.

Now, we can find the weight of the dog using either of the two original equations. Let's use the second equation:

D = C + 22

D = 12 + 22

D = 34

So, the weight of the dog is 34 pounds.

Therefore, the dog weighs 34 pounds, and the cat weighs 12 pounds.

144 is the _ power of 12

Answers

Answer:

144 is the second power of 12

Step-by-step explanation:

Here, we want to get the power of 12 that 144 is

Mathematically;

144 = 12^2

What this mean is that we have to raise 12 to 2 to get 144

Thus, our answer is that 144 is the 2nd power of 12