kiran has 27 nickels and quarters in his pocket, worth a total of $2.75. solve the system of equations to…

kiran has 27 nickels and quarters in his pocket, worth a total of $2.75. solve the system of equations to show how many nickels and quarters are in kirans pocket. how many nickels? make sure to label your answers clearly.

kiran has 27 nickels and quarters in his pocket, worth a total of $2.75. solve the system of equations to show how many nickels and quarters are in kirans pocket. how many nickels? make sure to label your answers clearly.

Answer

Answer:

25 nickels

Explanation:

Step1: Set up equations

Let $n$ be number of nickels, $q$ be number of quarters. $n + q=27$ (total number of coins), $0.05n + 0.25q = 2.75$ (total value).

Step2: Express $q$ from first equation

$q = 27 - n$.

Step3: Substitute into second equation

$0.05n+0.25(27 - n)=2.75$. Expand: $0.05n + 6.75-0.25n=2.75$.

Step4: Simplify equation

Combine like terms: $- 0.2n=2.75 - 6.75$. $-0.2n=-4$.

Step5: Solve for $n$

$n=\frac{-4}{-0.2}=20$. (Wait, there was a miscalculation. Let's start again.)

Let $n$ be nickels, $q$ be quarters. Equations:

  1. $n + q=27$ (count)
  2. $0.05n+0.25q = 2.75$ (value)

From equation 1: $q = 27 - n$.

Substitute into equation 2: $0.05n+0.25(27 - n)=2.75$ $0.05n+6.75 - 0.25n=2.75$ $-0.2n=2.75 - 6.75$ $-0.2n=-4$ $n = 20$ (Wrong, let's check units. $2.75$ is $275$ cents. $n + q=27$, $5n+25q=275$)

Let $n$ (nickels: 5 - cent) and $q$ (quarters: 25 - cent) $n + q=27$ (equation A) $5n + 25q=275$ (equation B)

From A: $q = 27 - n$

Substitute into B: $5n+25(27 - n)=275$ $5n+675 - 25n=275$ $-20n=275 - 675$ $-20n=-400$ $n = 20$ (No, wait $20$ nickels ($1$ dollar) and $7$ quarters ($1.75$) sum to $2.75$. But wait, $20 + 7=27$. So nickels: 20.

Wait, no: Let $x$ be nickels, $y$ be quarters. $x + y=27$ $5x + 25y=275$ (since $2.75$ dollars = 275 cents)

From first equation: $y = 27 - x$

Substitute into second: $5x+25(27 - x)=275$ $5x + 675-25x=275$ $-20x=275 - 675$ $-20x=-400$ $x = 20$.

But wait: $20$ nickels ($20\times5 = 100$ cents) and $7$ quarters ($7\times25=175$ cents). $100 + 175=275$ cents ($2.75$ dollars) and $20 + 7=27$ coins.

So number of nickels: 20.

Another way: Let’s assume all 27 coins are quarters. Value would be $27\times0.25 = 6.75$ dollars.

Difference between assumed value ($6.75$) and actual ($2.75$) is $6.75 - 2.75 = 4$ dollars.

Each replacement of a quarter with a nickel reduces value by $0.25 - 0.05=0.2$ dollars.

Number of nickels: $\frac{4}{0.2}=20$.