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Nina [5.8K]
3 years ago
15

At a party, the amount of people who ate meatballs was 9 less than 3/5 of the total number of people. The number of people who a

te meatballs was 24. How many people where at the party? Write an equation to help you solve the problem. Let x represent the number of people at the party.
Mathematics
1 answer:
Luda [366]3 years ago
3 0

Answer:

there were a total of 55 people at the party.

Step-by-step explanation:

In order to create the equation representing this scenario we first need to represent each step in a formula. Since the total number of people is represented by x we can multiply 3/5 by x and subtract 9 from that. This would then be equal to 24 like so...

3/5x - 9 = 24

Now that we have the formula we can perform opposite operations to isolate x and solve for it.

3/5x - 9 = 24   ... add 9 on both sides

3/5x = 33   ... divide both sides by 3/5

x = 55

Finally, we can see that there were a total of 55 people at the party.

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Let's deal with each factor in the numerator individually first: when evaluating the power of a power, you have to multiply the exponents: (a^b)^c = a^{bc}

So, we have

[tex](3^2)^{-\frac{1}{2}} = 3^{2\cdot(-\frac{1}{2})} = 3^{-1},\quad (9^4)^{-1} = 9^{-4}

Now remember that 9=3^2 and 27=3^3 to rewrite the expression as

\dfrac{3^{-1}\cdot (3^2)^{-4}}{(3^3)^{-3}} = \dfrac{3^{-1}\cdot 3^{-8}}{3^{-9}}

Now use the rules

a^b\cdot a^c = a^{b+c},\quad \dfrac{a^b}{a^c} = a^{b-c}

to conclude

\dfrac{3^{-1}\cdot 3^{-8}}{3^{-9}} = 3^{-1-8-(-9) = 3^0 = 1

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