Martina, hong, and felipe sent a total of 91 text messages over their cell phones during the weekend. hong sent 9 more messages than martina. felipe sent 2 times as many messages as hong. how many messages did they each send?

M = 16

H = 25

F = 50

Step-by-step explanation:

Let's use for abbreviation M for Martina's messages, H for Hong's messages and F for Felipe's messages.

Now we need to write the given information as equations.

Martina, Hong, and Felipe sent a total of 91 text messages

(1) M + H + F = 91

Hong sent 9 more messages than Martina.

(2) H = M + 9

Felipe sent 2 times as many messages as Hong

(3) F = 2 * H

Now with this system, we need to replace the letters to leave only M in the first equation.

(4) M + (M + 9) + (2*(M + 9)  = 91

(5) 4*M + 27 = 91

(6) M = (91-27) / 4

Then we find the

M = 16

H = 25

F = 50

m∠cdf = 43° , m∠gdf = 114°, m∠gde = 23°, m∠edh = 23° , m∠cdh = 157°

step-by-step explanation:

since, it is given that de bisects the angle gdh ⇒ de divides the angle gdh into two equal angles.

⇒ m∠gde = m∠edh

⇒ 8·x   - 1 = 6·x + 5

⇒ x = 3

so, m∠gde = 8·x - 1 = 23°

and m∠edh = 23°

now, it is given ∠cde is an straight angle so, m∠cde = 180°

⇒ m∠cdf + m∠fdg + m∠gde = 180°

⇒ 43° + m∠fdg + 23° = 180°

⇒ m∠fdg = 114°

again, m∠cde = m∠cdh + m∠edh = 180°

m∠cdh + 23° = 180°

⇒ m∠cdh = 157°

6 cm

step-by-step explanation: