Given. Question Taylor has 25.00 in dimes and quarters. She...

given. Question Taylor has $25.00 in dimes and quarters. She has 40 more dimes than quarters. If \textit{x} represents the number of quarters that Taylor has, which of the following is an equation that represents the total value of her dimes and quarters? $\circ$ .10(\textit{x} + 40) + .25\textit{x} = 2.500 $\circ$ 10\textit{x} + .25(\textit{x} + 40) = 2.500 $\circ$ 10(40 - \textit{x}) + 25\textit{x} = 2.500 $\circ$ 10(\textit{x} + 40) + 25\textit{x} = 2.500

Transcript

00:01 Okay, viviana has a pocket full of money, and we know it's $2 made up of nickels, dimes, and quarters.

00:15 So what i'm going to do is i'm going to set up some variables.

00:17 I'm going to say n equals number of nickels, d equals number of dants, and q equals number of quarters.

00:29 They tell me she has 18 total coins, so i know that n plus d plus q has to equal 18.

00:46 They also tell me that the number of nickels equals 25 minus twice the number of dimes.

00:54 Okay, so the number of nickels equals 25 minus twice the number of dimes, which i don't know.

01:08 Say dimes.

01:09 Oops, and this should be nickels.

01:11 I'm sorry.

01:13 The number of nickels equals 25 minus the number, twice the number of dimes.

01:20 Okay, so here's my second equation.

01:22 Here's first one, second one.

01:25 And then last but not least, we know she has that $2.

01:28 So here's where i'm going to take the money part in.

01:31 My nickels are worth $0 .5 a piece, and i have n of them.

01:37 My dimes are worth $0 .10.

01:39 And i have d of them, and my quarters are worth 0 .25 cents apiece, and i have q of them, and that all needs to equal two.

01:50 Now, this equation is a good one, but to avoid decimals, what we can do is just multiply everything by 100, and that will clear out all our decimals.

02:00 So my new third equation will be 200 equals 5n plus 10d plus 25, q, which is a lot easier to work with than the one we had.

02:14 All right, so i'm going to piece these three equations together.

02:18 This one would be nice to plug into this one by substitution because it will allow me to get rid of one of the variables.

02:26 So i'm going to go ahead and do that, and i'm going to rewrite n plus d plus q equals 18 as instead of n25 minus 2d plus d plus d plus d.

02:40 Plus q equals 18.

02:43 So now i'm looking at 25 minus d plus q equals 18, or even better, negative d plus q equals negative 7...

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