Question 1202342
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Answers:
<font color=red>14 nickels, 20 dimes</font>



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Work Shown:


Method 1


n = number of nickels
34-n = number of dimes


5n = value of the nickels (cents)
10(34-n) = 340-10n = value of the dimes (cents)
5n+340-10n = -5n+340 = total value (cents)


$2.70 = 2.70*100 = 270 cents


-5n+340 = 270
-5n = 270-340
-5n = -70
n = -70/(-5)
n = 14
They have <font color=red>14 nickels</font>


And also
34-n = 34-14 = <font color=red>20 dimes</font>


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Method 2


Let's say we start with all 34 coins as nickels
34 nickels = 34*5 = 170 cents


The gap from 170 cents to the target goal of 270 cents is 270-170 = 100 cents.
To get to the target, we'll need to replace some nickels with dimes.


Each time we replace a nickel with a dime, the net value increase is 5 cents (because 10 cents - 5 cents = 5 cents)


Let x be the number of times we replace a nickel with a dime.
5x then represents the total net increase. We want this to equal the 100 cents calculated earlier.


5x = 100
x = 100/5
x = 20
We must replace 20 nickels with 20 dimes


34 nickels drops to 34-20 = <font color=red>14 nickels</font>
0 dimes increases to 0+20 = <font color=red>20 dimes</font>


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Check:


14 nickels + 20 dimes = 34 coins total
That validates the coin count requirement.


A = 14 nickels = 14*5 = 70 cents
B = 20 dimes = 20*10 = 200 cents
A+B = 70 cents + 200 cents = 270 cents = $2.70
That validates the total value requirement.


Both conditions have been met. The answers are confirmed.
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