For every 4 girls that preferred a lighter shade of blue jeans, 3 girls preferred a darker shade. If a total of 210 girls were surveyed, how many chose the lighter shade? Justify your reasoning by applying relevant strategies to solve the problem.

120 girls chose the lighter shade

Step-by-step explanation:

For every 4 girls that preferred a lighter shade of blue jeans, 3 girls preferred a darker shade.

This question has to do with ratio and proportions.

For every 4 girls that preferred a lighter shade of blue jeans, 3 girls preferred a darker shade.

We have a ratio of Lighter shade to darker shade

Lighter shade: Darker shade

= 4:3

Sum of proportions = 4 + 3 = 7

Total number surveyed = 210

If a total of 210 girls were surveyed, how many chose the lighter shade?

This is calculated as:

4/7 × 210 girls

= 120 girls

Therefore, 120 girls chose the lighter shade

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)