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Martin has a combination of 33 quarters and dimes worth a total of [tex]$\$[/tex]6[tex]$. Which system of linear equations can be used to find the number of quarters, $[/tex]q[tex]$, and the number of dimes, $[/tex]d$, Martin has?

A.
[tex]\[
\begin{array}{l}
q + d = 6 \\
25q + 10d = 33
\end{array}
\][/tex]

B.
[tex]\[
\begin{array}{l}
q + d = 6 \\
0.25q + 0.1d = 33
\end{array}
\][/tex]

C.
[tex]\[
\begin{array}{l}
q + d = 33 \\
25q + 10d = 6
\end{array}
\][/tex]

D.
[tex]\[
\begin{array}{l}
q + d = 33 \\
0.25q + 0.1d = 6
\end{array}
\][/tex]



Answer :

GinnyAnswer
Let's solve this step-by-step by translating the information given into a system of linear equations.

1. First equation: Total number of coins

Martin has a combination of quarters and dimes that adds up to 33 coins. This equates to:

[tex]\[ q + d = 33 \][/tex]

where [tex]\( q \)[/tex] represents the number of quarters and [tex]\( d \)[/tex] represents the number of dimes.

2. Second equation: Total value of coins

The total value of these quarters and dimes is [tex]$6. Since the value of a quarter is 25 cents and the value of a dime is 10 cents, the total value can be expressed as: \[ 25q + 10d = 600 \] Here, we converted $[/tex]6 into cents to match the units with the coin values. $6 is equivalent to 600 cents (1 dollar = 100 cents).

Therefore, the system of linear equations that can be used to determine the number of quarters ([tex]\( q \)[/tex]) and dimes ([tex]\( d \)[/tex]) Martin has is:

[tex]\[ \begin{array}{l} q + d = 33 \\ 25q + 10d = 600 \end{array} \][/tex]

Thus, the correct option is:

[tex]\[ \begin{array}{l} q + d = 33 \\ 25q + 10d = 600 \end{array} \][/tex]

Answer:Let's denote:

The number of quarters as

q.

The number of dimes as

d.

We are given two pieces of information:

Step-by-step explanation:Martin has a total of 33 quarters and dimes:

+

=

33

q+d=33

The total value of the quarters and dimes is $6.00. The value of a quarter is $0.25, and the value of a dime is $0.10:

0.25

+

0.10

=

6

0.25q+0.10d=6

So the system of linear equations that can be used to find the number of quarters and dimes is:

+

=

33

0.25

+

0.10

=

6

q+d

0.25q+0.10d

​

 

=33

=6

​

Would you like to solve this system of equations?

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