Susan, Hong, and Juan sent a total of 107 text messages over their cell phones during the weekend. Hong sent 4 times as many messages as Juan. Juan sent 5 fewer messages than Susan. How many messages did they each send?

X: Nb of Susan’s texts

4(x-5)+(x-5)+x= 107
Isolate X
X=107

Replace X with 22 in each equation to find out the number of texts

Susan: 22 Texts ( x )
Hong: 68 Texts 4( x-5 )
Juan: 17 Texts ( x-5 )

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Favouredlyf Favouredlyf · Answer 2 · 2019-12-22T15:47:59+01:00

Answer: susan sent 22 texts

Hong sent 68 texts

Juan sent 17 texts

Step-by-step explanation:

Let x represent the number of text messages that Susan sent during the weekend.

Let y represent the number of text messages that Hong sent during the weekend.

Let z represent the number of text messages that Juan sent during the weekend.

Susan, Hong, and Juan sent a total of 107 text messages over their cell phones during the weekend. This means that

x + y + z = 107 - - - - - - - - 1

Hong sent 4 times as many messages as Juan. This means that

y = 4z

Juan sent 5 fewer messages than Susan. This means that

x = z + 5

Substituting y = 4z and x = z + 5 into equation 1, it becomes

z + 5 + 4z + z = 107

z + 4z + z = 107 - 5

6z= 102

z = 102/6 = 17

x = z + 5 = 17 + 5 = 22

y = 4z = 17×4 = 68