E) 340 people participated in a conference. If the ratio of ladies and gentleman is 3:2, find the number of ladies and gentlemen in the conference.

There were 204 ladies and 136 gentlemen in the conference

Step-by-step explanation:

Let's set the variables:

L = number of ladies in the conference

G = number of gentlemen in the conference

We know 340 people participated in the conference, thus:

L + G = 340         [1]

We are also given the ratio of ladies and gentleman as 3:2, thus:

L/G = 3/2

Cross-multiplying:

2L = 3G        [2]

From [1]:

L = 340 - G

Substituting in [2]:

2(340 - G) = 3G

Operating:

680 - 2G = 3G

5G = 680

G = 680/5 = 136

G = 136

L = 340 - 136 = 204

L = 204

There were 204 ladies and 136 gentlemen in the conference

3< x< 5

step-by-step explanation:

|x - 4| < 1

there are two solutions, one positive and one negative.   remember to flip the inequality when taking the negative solution

x-4 < 1       x-4 > -1

add 4 to each side

x-4+4 < 1+4       x-4+4 > -1+4

x< 5                 x> 3

3< x< 5

yes   because as the functions are graphed they eventually will intersect unless otherwise

step-by-step explanation: