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Answer :
To determine the correct equation that describes the possible combinations of quarters and nickels Miranda has in her piggy bank, we need to consider the value of each type of coin:
- A quarter is worth 25 cents.
- A nickel is worth 5 cents.
Miranda has a total of $3.60 in her piggy bank, which is equal to 360 cents. We need an equation that sums up the value of quarters and nickels to equal this total. Let's set up the equation using `q` to represent the number of quarters and `n` to represent the number of nickels.
For quarters:
- Each quarter contributes 25 cents, so quarters contribute a total of [tex]\(25q\)[/tex] cents to the total.
For nickels:
- Each nickel contributes 5 cents, so nickels contribute a total of [tex]\(5n\)[/tex] cents to the total.
The entire amount of money Miranda has in her piggy bank is the sum of the values of the quarters and nickels, which must equal 360 cents. So, the equation we can set up is:
[tex]\[ 360 = 25q + 5n \][/tex]
This equation allows us to find different combinations of quarters and nickels where the total value is 360 cents. By solving this equation for integer values of [tex]\(q\)[/tex] and [tex]\(n\)[/tex], we can determine the possible numbers of quarters and nickels Miranda has.
- A quarter is worth 25 cents.
- A nickel is worth 5 cents.
Miranda has a total of $3.60 in her piggy bank, which is equal to 360 cents. We need an equation that sums up the value of quarters and nickels to equal this total. Let's set up the equation using `q` to represent the number of quarters and `n` to represent the number of nickels.
For quarters:
- Each quarter contributes 25 cents, so quarters contribute a total of [tex]\(25q\)[/tex] cents to the total.
For nickels:
- Each nickel contributes 5 cents, so nickels contribute a total of [tex]\(5n\)[/tex] cents to the total.
The entire amount of money Miranda has in her piggy bank is the sum of the values of the quarters and nickels, which must equal 360 cents. So, the equation we can set up is:
[tex]\[ 360 = 25q + 5n \][/tex]
This equation allows us to find different combinations of quarters and nickels where the total value is 360 cents. By solving this equation for integer values of [tex]\(q\)[/tex] and [tex]\(n\)[/tex], we can determine the possible numbers of quarters and nickels Miranda has.
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