Christina B. answered • 08/27/19
Experienced, Positive, and Effective Tutor with an M.Ed.
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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