Oscar has twice as many pennies than he has dimes. All together he has $.84. How many dimes and pennies does he have?
I tried to solve this, but I know I did it wrong, because I got a decimal for the amount of dimes. Here's what I did:
P=D*2
(.01)(P)+(.10)(D)=.84
(.01)(D*2)+(.10)(D)=.84
.01D+.02+.10D=.84
.11D+.02=.84
-.02-.02
____________
.11D+ 0 =.82
____ ___
.11 .11
And this is where I stopped because I got the decimal. Could you guys please help?? Thanks.
X Dimes.
2x Pennies.
10*x + 1*2x = 84 Cents.
12x = 84.
X = 7 Dimes.
2x = 2*7 = 14 Pennies.
Hmmm. How did you get through this step?
(.01)(D*2)+(.10)(D)=.84
.01D+.02+.10D=.84
To avoid the decimals:
$1.00 = 100 Cents.
$0.84 = 84 Cents.
0.01 = 1 Cent.
To solve this problem correctly, let's go through the steps again:
Let P represent the number of pennies and D represent the number of dimes.
First, we can set up the equation based on the given information:
1. The number of pennies (P) is twice the number of dimes (D): P = 2D.
2. The total value of all the coins is 84 cents: 0.01P + 0.10D = 0.84.
Now we can substitute P = 2D into the second equation:
0.01(2D) + 0.10D = 0.84.
0.02D + 0.10D = 0.84.
0.12D = 0.84.
Dividing both sides by 0.12:
D = 0.84 / 0.12.
D = 7.
We have found the value for D, which represents the number of dimes. To find the number of pennies (P), we substitute D = 7 into the first equation:
P = 2(7).
P = 14.
So, Oscar has 7 dimes and 14 pennies.