SOLUTION: I am a grandmother whose granddaughter has asked for help. Can you provide me with the type of equation I can use to explain to her how to calculate the answer to the following?

Question 774423: I am a grandmother whose granddaughter has asked for help. Can you provide me with the type of equation I can use to explain to her how to calculate the answer to the following? "Mr. Charles cashed a $135 check. He received $5 bills and $10 bills. The number of $5 bills was 3 more than twice the number of $10 bills. How many bills of each type did Mr. Charles receive. I know the answer using elimination, but want to give her a formula she can use going forward. Thank you
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Charles cashed a $135 check.
He received $5 bills and $10 bills.
The number of $5 bills was 3 more than twice the number of $10 bills.
How many bills of each type did Mr. Charles receive. ]
:
let f = no. of fives
let t = no. of 10s
:
Write an equation for each statement:
:
"Charles cashed a $135 check. He received $5 bills and $10 bills."
5f + 10t = 135
:
The number of $5 bills was 3 more than twice the number of $10 bills.
f = 2t + 3
f - 2t = 3; use this form for elimination
multiply the above equation by 5, add to the 1st equation
5f - 10t = 15
5f + 10t = 135
-------------------adding eliminates t, find f
10f = 150
f = 150/10
f = 15 fives
:
then using the 1st equation, replace f with 15
5(15) + 10t = 135
75 + 10t = 135
10t = 135 - 75
10t = 60
t = 60/10
t = 6 tens
:
:
Confirm this using the 2nd equation, f = 2t + 3
15 = 2(6) + 3

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