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lyudmila [28]
3 years ago
15

At Harriet Tubman middle school, there are 85 students in the 7th grade . The number of girls is 1 1/2 times the number of boys.

How many girls and how many boys are in the 7th grade?
Mathematics
1 answer:
tatuchka [14]3 years ago
5 0

Answer:

Number of boys in 7th grade=34 boys

Number of girls in 7th grade=51 girls

Step-by-step explanation:

Total Number of students in 7th grade=Number of boys+Number of girls

where;

Total number of students in 7th grade=85 students

Number of boys=x

Number of girls=(1 1/2)×Number of boys=(3/2)×x=1.5x

Replacing;

85=x+1.5x

2.5x=85

x=85/2.5

x=34

Number of boys=x=34

Number of girls=1.5x=1.5×34=51

Number of boys in 7th grade=34 boys

Number of girls in 7th grade=51 girls

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Luisa is planning a bridal shower for her best friend. At the party, she wants to serve 3 beverages, 3 appetizers, and 3 dessert
Vladimir79 [104]

Answer:

Luisa can pick the food and drinks to serve at the bridal shower in 15,615,600 different ways.

Step-by-step explanation:

Fundamental counting principle:

States that if there are p ways to do a thing, and q ways to do another thing, and these two things are independent, there are p*q ways to do both things.

Also

The order in which the food and drinks are chosen is not important, which means that the combinations formula is used to solve this question.

Combinations formula:

C_{n,x} is the number of different combinations of x objects from a set of n elements, given by the following formula.

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3 from a set of 15. So

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Desserts:

3 from a set of 13. So

D = C_{13,3} = \frac{13!}{3!10!} = 286

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By the fundamental counting principle, as beverages, appetizers and desserts are independent:

T = B*A*D = 455*120*286 = 15,615,600

Luisa can pick the food and drinks to serve at the bridal shower in 15,615,600 different ways.

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