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Sagot :
Let's break down the problem step-by-step to find the appropriate system of equations that Regina could use.
1. Initial Savings and Additional Monthly Savings:
- Regina starts with \[tex]$500 in her savings account. - She saves an additional \$[/tex]75 each month.
We can create an equation to represent the total amount of savings [tex]\(y\)[/tex] Regina will have after [tex]\(x\)[/tex] months. This will include her initial savings plus the additional monthly savings:
[tex]\[ y = 75x + 500 \][/tex]
2. Loan Amount and Monthly Payments:
- Regina takes out a loan of \[tex]$1,600 for the washer and dryer set. - She makes monthly payments of \$[/tex]134.
We can create another equation to represent the remaining loan amount [tex]\(y\)[/tex] after [tex]\(x\)[/tex] months. This will include the initial loan amount minus the total monthly payments made:
[tex]\[ y = 1600 - 134x \][/tex]
Now we need to match these equations with the given options:
- Option A:
[tex]\[ y = 134x + 500 \][/tex]
[tex]\[ y = 1600 - 100x \][/tex]
- Option B:
[tex]\[ y = 75x + 500 \][/tex]
[tex]\[ y = 1600 - 134x \][/tex]
- Option C:
[tex]\[ y = 500x + 75 \][/tex]
[tex]\[ y = 1600 - 134x \][/tex]
- Option D:
[tex]\[ y = 1600x + 134 \][/tex]
[tex]\[ y = 75x - 500 \][/tex]
By comparing our derived equations [tex]\(y = 75x + 500\)[/tex] and [tex]\(y = 1600 - 134x\)[/tex] with the provided options, we see that the equations match Option B.
Therefore, the correct system of equations that Regina should use is:
[tex]\[ \boxed{y = 75x + 500} \][/tex]
[tex]\[ \boxed{y = 1600 - 134x} \][/tex]
1. Initial Savings and Additional Monthly Savings:
- Regina starts with \[tex]$500 in her savings account. - She saves an additional \$[/tex]75 each month.
We can create an equation to represent the total amount of savings [tex]\(y\)[/tex] Regina will have after [tex]\(x\)[/tex] months. This will include her initial savings plus the additional monthly savings:
[tex]\[ y = 75x + 500 \][/tex]
2. Loan Amount and Monthly Payments:
- Regina takes out a loan of \[tex]$1,600 for the washer and dryer set. - She makes monthly payments of \$[/tex]134.
We can create another equation to represent the remaining loan amount [tex]\(y\)[/tex] after [tex]\(x\)[/tex] months. This will include the initial loan amount minus the total monthly payments made:
[tex]\[ y = 1600 - 134x \][/tex]
Now we need to match these equations with the given options:
- Option A:
[tex]\[ y = 134x + 500 \][/tex]
[tex]\[ y = 1600 - 100x \][/tex]
- Option B:
[tex]\[ y = 75x + 500 \][/tex]
[tex]\[ y = 1600 - 134x \][/tex]
- Option C:
[tex]\[ y = 500x + 75 \][/tex]
[tex]\[ y = 1600 - 134x \][/tex]
- Option D:
[tex]\[ y = 1600x + 134 \][/tex]
[tex]\[ y = 75x - 500 \][/tex]
By comparing our derived equations [tex]\(y = 75x + 500\)[/tex] and [tex]\(y = 1600 - 134x\)[/tex] with the provided options, we see that the equations match Option B.
Therefore, the correct system of equations that Regina should use is:
[tex]\[ \boxed{y = 75x + 500} \][/tex]
[tex]\[ \boxed{y = 1600 - 134x} \][/tex]
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