Write a real-world problem that can be modeled by the inequality 10x > 5.5x + 31.5

Kim and Jane invested the same amount in two different types of investment plans.

After a certain period, Kim earned 10 times of what he invested and Jane earned $31.5 more than 5.5 times of the money she invested.

If Kim's earning is more than Jane's earning, find the minimum amount they invested at the beginning.

Let x be the money they invested at the beginning.

So, after a certain period,

Kim's earnings = 10x and

Jane's earnings = 5.5x + 31.5

Since Kim earned more than Jane,

10x > 5.5x + 31.5.

75 tickets have been sold so far.

step-by-step explanation:

in this question it is clearly mentioned that 45 children's tickets have been sold and this number is 60% of the total tickets sold.

now let's assume the total number of tickets sold be x.

then 60% of x = 45

⇒

⇒ x(.6) = 45

by dividing with .6 on both the sides of the equation

⇒ x = 75

therefore 75 tickets have been sold so far.

the correct option is 2.

step-by-step explanation:

according to the given information triangle abc is a right angle triangle with right angle at a. segment ab is 5 and segment ac is 7. point d is on segment bc and angles adb and adc are right angles.

it is given that triangles abd, cad, and cba are similar.

two triangles are similar if their corresponding sides are proportional.

in triangle cba, using pythagoras theorem

                      )

triangle abd and cba are similar,

                            (2)

triangle cad and cba are similar,

                      )

using (1), (2) and (3), we get

hence proved.

therefore option 2 is correct.