Question

Emilio has 6 more nickels than dimes, and the total value of his coins is $2.10. How many nickels does he have? Let n represent the number of nickels
0.10n + 0.05n + 6 = 2.10

0.10n + 0.05(n + 6) = 2.10

0.10(n + 6) + 0.05n = 2.10

0.10(n 6) + 0.05n = 2.10

Answer 1

6 more nickles than dimes, hmm so let's try to write this as an equation.
let N be nickels, D be dimes.

N + 6 = D <-- Nickles plus 6 more equals the number of dimes.

We'll have to make another equation, based on the VALUE of the coins.

Dimes are worth 10 cents each. So if we have D dime, we can write it like this,
.10D <-- This represents the value of D dimes.

Doing the same with nickles gives us,
.05N <-- The value of N nickles

We'll make an equation out of the TOTAL VALUE of the coins that they gave us at the start.

All of the coins should add up to $2.10.
N nickles plus D dimes (at their respective values) should add up to 2.10.
We can write this as,

.05N + .10D = 2.10

So we have a system of equations,\[\huge N+6=D\]
\[\huge .05N+.10D=2.10\]

Does this much make sense so far?

Answer 2

these are the options for question
0.10n + 0.05n + 6 = 2.10

0.10n + 0.05(n + 6) = 2.10

0.10(n + 6) + 0.05n = 2.10

0.10(n 6) + 0.05n = 2.10

Answer 3

Did I do the first one backwards? Maybe it's suppose to be N=D+6, my brain might be thinking a little cooky today :)

Answer 4

there is no d unfortunately

Answer 5

ill edit my question

Answer 6

We need to take this system, and combine them, to give us one equation involving N. I just wanna make sure I didn't make a silly mistake real quick.

Yah it should be N=D+6, my bad.
Which we can rewrite as N-6=D

We want to plug in this value for the D in the other equation.

\[\large N-6=(D)\]\[\large .05N+.10(D)=2.10 \qquad \rightarrow \qquad .05N+.10(N-6)=2.10\]

Answer 7

What is the last option? the symbol isn't showing up

Answer 8

minus