One serving of Mike’s crackers has 150 calories and a mass of 30 grams. How many calories are in 6 grams of the crackers?

1 answer:

3 0

$\bf \begin{array}{ccll}
calories&grams\\
\text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\
150&30\\
c&6
\end{array}\implies \cfrac{150}{c}=\cfrac{30}{6}\implies \cfrac{150\cdot 6}{30}=c$

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On the last day of school, Mrs. Awesome gave jelly beans to her class. She gave each boy as many jelly beans as there were boys

professor190 [17]

Answer:

28 students

Step-by-step explanation:

Let x be the number of girls in the class. There were two more boys than girls in her class, then the number of boys is x + 2.

Mrs. Awesome gave each boy as many jelly beans as there were boys in the class, so each of x + 2 boys got x + 2 jelly beans, so

Number of boys = x + 2

Number of jelly beans each boy got = x + 2

Total number of jelly beans all boys got = (x + 2)(x + 2)

Mrs. Awesome gave each girl as many jelly beans as there were girls in the class, so each of x girls got x jelly beans, so

Number of girls = x

Number of jelly beans each girl got = x

Total number of jelly beans all girls got = (x)(x)

Hence,

Total number of jelly beans class got = (x + 2)(x + 2) + (x)(x)

Mrs. Awesome brought 400 jelly beans, and when she finished, she had six jelly beans left, so she gave 400 - 6 = 394 jelly beans to the calss.

So,

$(x+2)(x+2)+(x)(x)=394\\ \\x^2+2x+2x+4+x^2=394\\ \\2x^2+4x+4-394=0\\ \\2x^2+4x-390=0\\ \\x^2+2x-195=0\\ \\D=2^2-4\cdot (-195)=4+780=784\\ \\\sqrt{D}=28\\ \\x_{1,2}=\dfrac{-2\pm 28}{2\cdot 1}=-15,\ 13$