Question

Kat has 19 coins, all quarters and dimes, that are worth a total of $4. The system of equations that can be used to find the number of quarters, q, and the number of dimes, d, she has is shown. q + d = 19 0.25q + 0.1d = 4 How many quarters does she have?

Answer 1

She has 14 quarters.

Explanation

The given system of equations is...........

$q+d=19 ............................(1)\\ \\ 0.25q+0.1d= 4 ...........................(2)$

here $q$ is the number of quarters and  $d$ is the number of dimes.

First, we will multiply equation (1) by  $-0.1$, so we will get...........

$-0.1q-0.1d= -1.9 ................................(3)$

Now, adding equation (2) and (3) , we will get.............

$0.25q-0.1q= 4-1.9\\ \\ 0.15q=2.1\\ \\ q=\frac{2.1}{0.15}= 14$

So, she has 14 quarters.

Answer 2

Answer:

she has 14 quarters.

Step-by-step explanation:

The given system of equations is...........

\begin{lgathered}q+d=19 ............................(1)\\ \\ 0.25q+0.1d= 4 ...........................(2)\end{lgathered}

q+d=19............................(1)

0.25q+0.1d=4...........................(2)

here qq is the number of quarters and dd is the number of dimes.

First, we will multiply equation (1) by -0.1−0.1 , so we will get...........

-0.1q-0.1d= -1.9 ................................(3)−0.1q−0.1d=−1.9................................(3)

Now, adding equation (2) and (3) , we will get.............

\begin{lgathered}0.25q-0.1q= 4-1.9\\ \\ 0.15q=2.1\\ \\ q=\frac{2.1}{0.15}= 14\end{lgathered}

0.25q−0.1q=4−1.9

0.15q=2.1

q=

0.15

2.1

=14

So, she has 14 quarters.

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