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Sagot :
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]
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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