Jasina has a total of $\$ 0.80$ in nickels and dimes, and she has $4$ more nickels than dimes. Which of the following systems of equations can be used to find out how many $n$ nickels and $d$ dimes she has? $\newline$ Choose $1$ answer: $\newline$ (A) $d+n=4$ $\newline$ $0.1 d+0.05 n=0.8$ $\newline$ (B) $d+4=n$ $\newline$ $0.1 d+0.05 n=0.8$ $\newline$ (c) $d-n=4$ $\newline$ $0.1 d+0.05 n=0.8$ $\newline$ (D) $n-d=-4$ $\newline$ $0.1 d+0.05 n=0.8$

Full solution

Q. Jasina has a total of

\$ 0.80

in nickels and dimes, and she has

4

more nickels than dimes. Which of the following systems of equations can be used to find out how many

n

nickels and

d

dimes she has?

\newline

Choose

1

answer:

\newline

(A)

d+n=4

\newline

0.1 d+0.05 n=0.8

\newline

(B)

d+4=n

\newline

0.1 d+0.05 n=0.8

\newline

(c)

d-n=4

\newline

0.1 d+0.05 n=0.8

\newline

(D)

n-d=-4

\newline

0.1 d+0.05 n=0.8

Identify Variables: question_prompt: Determine the correct system of equations to find the number of nickels and dimes Jasina has.
Write Equations: Step $1$ : Let's denote the number of dimes as $d$ and the number of nickels as $n$ . Since Jasina has $4$ more nickels than dimes, we can write the first equation as $n = d + 4$ .
Check Answer Choices: Step $2$ : The value of a dime is \$$0$.$10$ and the value of a nickel is \$$0$.$05$. Jasina has a total of \$$0$.$80$, so the second equation based on the total value is $0.10d + 0.05n = 0.80$.
Evaluate Choice (B): Step $3$: Now we need to check which answer choice matches our equations. Choice (A) doesn't match because $d + n = 4$ doesn't represent the relationship between the number of nickels and dimes.
Evaluate Choice (C): Step $4$: Choice (B) has the correct first equation $d + 4 = n$, which matches our equation $n = d + 4$ if we rearrange it. The second equation $0.1d + 0.05n = 0.8$ also matches our value equation.
Evaluate Choice (D): Step $5$: Choice (C) has the first equation $d - n = 4$, which is incorrect because it suggests that there are more dimes than nickels.
Evaluate Choice (D): Step $5$: Choice (C) has the first equation $d - n = 4$, which is incorrect because it suggests that there are more dimes than nickels. Step $6$: Choice (D) has the first equation $n - d = -4$, which is the opposite of what we need. The correct relationship is $n = d + 4$, not $n - d = -4$.