Robert has 96 balloons and 72 pieces of candy to make gift bags for his party. how many gift bags can he make if he wants to use all of the balloons and all of the candy?

  24

Step-by-step explanation:

The greatest common divisor of 72 and 96 is 24. Robert can make any number of bags that is a divisor of 24. If he wants to make the largest number possible, then he can make 24 bags with 4 balloons and 3 pieces of candy in each one.

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  72 = 2³·3²

  96 = 2⁵·3

The greatest common divisor is the product of the common factors: 2³·3 = 24.

x =±sqrt(1/3)

step-by-step explanation:

x+4/6x=1/x

multiply each side by 6x to get rid of the fractions

6x*(x+4/6x)=1/x*6x

distribute

6x^2 +4 = 6

subtract 4 from each side

6x^2 +4-4 = 6-4

6x^2 =2

divide by 6

6x^2/6 = 2/6

x^2 = 1/3

take the square root of each side

sqrt(x^2) = ±sqrt(1/3)

x =±sqrt(1/3)