Question 366301: Kesha had only pennies and dimes in her change purse. When she counted out her change, she had 54 cents. If she had 6 times as many pennies as she did dimes, how many pennies did she have?
I need an equation for this one and I started off with
p+d=54
d=6p
After this, i get stuck. I did it without an equation and got 24 pennies.
Found 2 solutions by josmiceli, Edwin McCravy:
Answer by josmiceli(19441)   (Show Source):
Answer by Edwin McCravy(20056)  (Show Source):
You can put this solution on YOUR website! Kesha had only pennies and dimes in her change purse. When she counted out her change, she had 54 cents. If she had 6 times as many pennies as she did dimes, how many pennies did she have?
I need an equation for this one and I started off with
p+d=54
d=6p
After this, i get stuck. I did it without an equation and got 24 pennies.
That's because you have both equation wrong. Also 54 should be 64. It comes
out fractions with 54, so it must have been 64.
To get money you can't add coins to coins.
You have p+d=54. Not only should the 54 be 64, but
pennies + dimes = cents
is senseless, it's like
apples + oranges = bananas.
Your equation must not be
copper coins + silver coins = amount of money.
You must have
amount of money + amount of money = amount of money
cents + cents = cents.
p pennies is worth p cents,
d dimes is worth 10p cents.
So your first equation is
p + 10d = 64, not p+d=64, and certainly not p+d=54
You also interpreted this clause wrong:
>>If she had 6 times as many pennies as she did dimes,<<
Notice these three examples:
If she had 2 dimes, she would have 12 pennies.
If she had 3 dimes, she would have 18 pennies
If she had 5 dimes, she would have 60 pennies.
So to get the number of pennies you must mutiply the number of dimes by 6.
So you have it backwards.
Its p=6d, not d=6p
So the two equation should be:
p+10d=64
p=6d
Substitute 6d for p in the first equation
6d+10d=64
16d=64
divide both sides by 16
d=4
Then since p=6d, p=6(4) = 24
So there are 3 dimes and 24 pennies.
Edwin
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