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Teresa, David, and Jose sent a total of 98 text messages over their cell phones during...

Teresa, David, and Jose sent a total of 98 text messages over their cell phones during the weekend. David sent more 10 messages than Teresa. Jose sent 4 times as many messages as David. How many messages did they each send?

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Answer #1

let

x = Teresa 's sent messages

y = David 's sent messages

z = Jose 's sent messages

Teresa, David, and Jose sent a total of 98 text messages

x+y+z=98..............(1)

David sent more 10 messages than Teresa

y=x+10

Jose sent 4 times as many messages as David z=4y

z=4y

z=4(x+10)

z=4x+40

put the value of y and z in equation 1

x+y+z=98

x+x+10+4x+40=98

6x+50=98

6x=48

x=48/6

x=8

.

y=x+10

y=8+10

y=18

.

.

z=4x+40

z=4(8)+40

z=32+40

z=72

x = 8 = Teresa 's sent messages

y = 18 = David 's sent messages

z = 72 = Jose 's sent messages

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