Josie makes fruit punch by mixing fruit juice and lemonade in the ratio 1:3

1 answer:

8 0

If she has three litres of fruit juice left, she can use nine liters of lemonade. She can make twelve more liters of punch

For the second batch the ratio of fruit juice to lemonade would be 3:12 or 1:4

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I have to determine whether the sides of the triangle form a pythagorean triple.

Crazy boy [7]

Answer:

Step-by-step explanation:

How do you know if side lengths form a Pythagorean triple?

Pythagorean triples may also help us to find the missing side of a right triangle faster. If two sides of a right triangle form part of a triple then we can know the value of the third side without having to calculate using the Pythagorean theorem. From the ratio, we know that it is a Pythagorean triple.

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Marco purchased a large box of comic books for $300. He gave 15 of the comic books to his brother and then sold the rest on an i

Yuri [45]

Answer: There are 75 books.

Price of each book = $4.

Step-by-step explanation:

Let x = Number of books in the box.

Then as per given,

Cost of x books = $300

Cost of one book = $\$(\dfrac{300}x)$

Books left after giving 15 of them = x-15

Selling price of (x-15) books= $330

Selling price of one book = $\$(\dfrac{330}{x-15})$

Profit on each book= $1.50

Profit = selling price - cost price

$\Rightarrow 1.50=\dfrac{330}{x-15}-\dfrac{300}{x}\\\\\Rightarrow\ 1.50=\dfrac{330(x)-300(x-15)}{x(x-15)}\\\\\Rightarrow\ 1.50=\dfrac{330x-300x+4500}{x^2-15x}\\\\\Rightarrow\ 1.50(x^2-15x)=30x+4500\\\\\Rightarrow\ 1.50x^2-22.5x=30x+4500\\\\\Rightarrow\ 1.50x^2-52.5x-4500=0\\\\\Rightarrow\ 1.50x^2-52.5x-4500=0\\\\\Rightarrow\ x^2-25x-3000=0\ \ [\text{divide by 1.5}]$