SOLUTION: I need help on making a system of equations based on a word problem. Here is the problem: Tricia and Michael share a cell phone plan, together; they made a total of 52 calls last m

Question 206048: I need help on making a system of equations based on a word problem. Here is the problem: Tricia and Michael share a cell phone plan, together; they made a total of 52 calls last month for a total of 620 minutes. Tricia averaged 15 minutes for each of her calls, while Michael averaged 10 minutes.
-How many calls did Tricia make last month?
-How many calls did Michael make last month?
Thank you for help.
Found 2 solutions by jim_thompson5910, stanbon:
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Let x = # of calls Tricia made and y = # of calls Michael made

Because "they made a total of 52 calls", this means that the sum of their calls will be 52. This means that

Since "Tricia averaged 15 minutes" per call, this means that she talked a total of minutes (ie multiply the time per call by the number of calls to get the total). Likewise, since "Michael averaged 10 minutes" per call, we know that Michael consumed minutes total. Add these totals up and set them equal to the final tally 620 to get:

So we now have the system of equations

I'll let you solve for x and y. Let me know if you still need help.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Tricia and Michael share a cell phone plan, together; they made a total of 52 calls last month for a total of 620 minutes. Tricia averaged 15 minutes for each of her calls, while Michael averaged 10 minutes.
-How many calls did Tricia make last month?

-How many calls did Michael make last month?
--------------------------------------------------------
Equations:
Quantity Eq.::: t + m = 52
Time Eq:::::::15t + 10m = 620
--------------------------------------
Multiply thru the 1st to set it up for elimination:
15t + 15m = 15*52
---
Subtract the 2nd equation from that and solve for "m":
5m = 15*52-620
m = 32 (# of calls Michael made)
---
Substitute into t+m=52 to solve for "t":
t + 32 = 52
t = 20 (# of calls Tricia made)
====================================
Cheers,
Stan H.

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