SOLUTION: Good evening.I would like to ask you to solve for these problems for me.. 1) A 60 feet piece of rope is cut into two pieces. One is 12 feet more than three times the other. Ho

Question 65415: Good evening.I would like to ask you to solve for these problems for me..
1) A 60 feet piece of rope is cut into two pieces. One is 12 feet more than three times the other. How long is each piece?
2) If there are 26 coins in a collection of dimes and quarters, and the value of the collection is $4.70, how many dimes and how many quarters are there?

Your best regard.
modi21
Answer by funmath(2933) (Show Source): You can put this solution on YOUR website!
Hi modi21
1) A 60 feet piece of rope is cut into two pieces. One is 12 feet more than three times the other. How long is each piece?
Let the "other peice" be: x
Then "one" is: 3x+12
The two peices added together is:60
(x)+(3x+12)=60
4x+12=60
4x+12-12=60-12
4x=48
4x/4=48/4
x=12
The "other Piece": x=12 ft
The "one": 3x+12=3(12)+12=36+12=48 ft
:
Sanity Check:
If you add the two pieces do you get 60 ft?
12+48=60
60=60 Yes. Looks ok.
:
2) If there are 26 coins in a collection of dimes and quarters, and the value of the collection is $4.70, how many dimes and how many quarters are there?
Let the number of quarters be: x
Then the rest of the coins are dimes: 26-x
Therefore, the amount of money (in cents) of quarters is: 25x
Therefore, the amount of money (in cents) of dimes is: 10(26-x)
The total amount of money (in cents) is: 470
25x+10(26-x)=470
25x+260-10x=470
15x+260=470
15x+260-260=470-260
15x=210
15x/15=210/15
x=14
The number of quarters: x=14
The number of dimes: 26-x=26-14=12
:
Sanity check:
If you have 14 quarters and 12 dimes, do you have $4.70?
14($.25)+12($.10)=$4.70
$3.50+$1.20=$4.70
$4.70=$4.70 It appears we're sane.
Happy Calculating!!!!
funmath
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