Inactive Tutor answered • 08/27/19
Hi Kirk,
We can use the information in this problem to set up several equations. Then we will solve the system of equations with substitution.
Lashonda, Tom and Bob sent a total of 71 text messages over their cell phones during the weekend. Tom sent 9 more messages than Lashonda. Bob sent 3 times as many messages as Tom.
L + T + B = 71
Lashonda, Tom and Bob sent a total of 71 text messages over their cell phones during the weekend. Tom sent 9 more messages than Lashonda. Bob sent 3 times as many messages as Tom.
T = L + 9
Lashonda, Tom and Bob sent a total of 71 text messages over their cell phones during the weekend. Tom sent 9 more messages than Lashonda. Bob sent 3 times as many messages as Tom.
B = 3T
Now we can go back to the first equation and start substituting:
L + T + B = 71
since T = L + 9, let's replace T in the equation:
L + (L + 9) + B = 71
We still have the tricky issue with the B, however. Let's see what we can do:
L + (L + 9) + B = 71
B = 3T
L + (L + 9) + 3T = 71
If we substitute one more time, we can convert everything to the same variable:
L + (L + 9) + 3T = 71
T = L + 9
L + (L + 9) + 3(L + 9) = 71
Now, you just need to simplify and solve for L.
L + (L + 9) + 3(L + 9) = 71
2L + 9 + 3L + 27 = 71
5L + 36 = 71
Once you've done that, you can plug your value for L back into T = L + 9 to find Tom's text messages. After that, you can solve for Bob's text messages using B = 3T. Check your work by making sure that all the values work in the L + T + B = 71 equation.
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