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) $d+n=4 \\ \quad 0.1 d+0.05 n=0.8$ $\newline$ (B) $d+4=n \\ \quad 0.1 d+0.05 n=0.8$ $\newline$ (C) $d-n=4 \\ \quad 0.1 d+0.05 n=0.8$ $\newline$ (D) $n-d=-4 \\ \quad 0.1 d+0.05 n=0.8$

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Grade 7

Solve two-step equations: word problems

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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 \\ \quad 0.1 d+0.05 n=0.8

\newline

(B)

d+4=n \\ \quad 0.1 d+0.05 n=0.8

\newline

(C)

d-n=4 \\ \quad 0.1 d+0.05 n=0.8

\newline

(D)

n-d=-4 \\ \quad 0.1 d+0.05 n=0.8

Translate Equation Relationship: Translate the information about the number of nickels and dimes into an equation. $\newline$ Jasina has $4$ more nickels than dimes. If we let $n$ represent the number of nickels and $d$ represent the number of dimes, then we can express this as $n = d + 4$ .
Translate Total Value Equation: Translate the information about the total value of nickels and dimes into an equation. $\newline$ Each nickel is worth $\$0.05$ and each dime is worth $\$0.10$ . The total value of the nickels and dimes is $\$0.80$ . This can be expressed as $0.05n + 0.10d = 0.80$ .
Identify Matching System of Equations: Identify the system of equations that matches the equations from Step $1$ and Step $2$ . $\newline$ We are looking for a system of equations that includes both the relationship between the number of nickels and dimes $n = d + 4$ and the total value of the nickels and dimes $0.05n + 0.10d = 0.80$ .
Compare Given Options: Compare the options given with the equations we have formed. $\newline$ Option (A) $d + n = 4$ and $0.1d + 0.05n = 0.8$ does not match our equations. $\newline$ Option (B) $d + 4 = n$ and $0.1d + 0.05n = 0.8$ matches our equations if we rearrange the first equation to $n = d + 4$ . $\newline$ Option (C) $d - n = 4$ and $0.1d + 0.05n = 0.8$ does not match our equations. $\newline$ Option (D) $n - d = -4$ and $0.1d + 0.05n = 0.8$ does not match our equations.
Select Correct Equations: Select the correct system of equations. $\newline$ The correct system of equations is given by Option (B) $d + 4 = n$ and $0.1d + 0.05n = 0.8$ , which matches the equations we derived from the problem statement.