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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? Choose 1 answer: (A) d+n=4 0.1 d+0.05 n=0.8 (B) d+4=n 0.1 d+0.05 n=0.8 (c) d-n=4 0.1 d+0.05 n=0.8 (D) n-d=-4 0.1 d+0.05 n=0.8

Jasina has a total of $0.80 \$ 0.80 in nickels and dimes, and she has 44 more nickels than dimes. Which of the following systems of equations can be used to find out how many n n nickels and d d dimes she has?\newlineChoose 11 answer:\newline(A) d+n=4 d+n=4 \newline0.1d+0.05n=0.8 0.1 d+0.05 n=0.8 \newline(B) d+4=n d+4=n \newline0.1d+0.05n=0.8 0.1 d+0.05 n=0.8 \newline(c) d−n=4 d-n=4 \newline0.1d+0.05n=0.8 0.1 d+0.05 n=0.8 \newline(D) n−d=−4 n-d=-4 \newline0.1d+0.05n=0.8 0.1 d+0.05 n=0.8

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Full solution

Q. Jasina has a total of $0.80 \$ 0.80 in nickels and dimes, and she has 44 more nickels than dimes. Which of the following systems of equations can be used to find out how many n n nickels and d d dimes she has?\newlineChoose 11 answer:\newline(A) d+n=4 d+n=4 \newline0.1d+0.05n=0.8 0.1 d+0.05 n=0.8 \newline(B) d+4=n d+4=n \newline0.1d+0.05n=0.8 0.1 d+0.05 n=0.8 \newline(c) d−n=4 d-n=4 \newline0.1d+0.05n=0.8 0.1 d+0.05 n=0.8 \newline(D) n−d=−4 n-d=-4 \newline0.1d+0.05n=0.8 0.1 d+0.05 n=0.8
  1. Identify Variables: question_prompt: Determine the correct system of equations to find the number of nickels and dimes Jasina has.
  2. Write Equations: Step 11: Let's denote the number of dimes as dd and the number of nickels as nn. Since Jasina has 44 more nickels than dimes, we can write the first equation as n=d+4n = d + 4.
  3. Check Answer Choices: Step 22: 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 \(0.10d + 0.05n = 0.80\).
  4. 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.
  5. 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.
  6. 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.
  7. 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 \(n - d = -4\).

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