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Faith baked a total of 192 muffins and cookies. After she sold \(\frac{2}{7}\) of her muffins and baked another 24 cookies, she had the same number of muffins and cookies. How many muffins did she bake at first?

Answer :

Let's solve this problem step-by-step using algebra.

First, let’s define some variables to represent the quantities in question:

  • Let [tex]M[/tex] be the number of muffins Faith baked initially.
  • Let [tex]C[/tex] be the number of cookies Faith initially baked.

According to the problem, Faith baked a total of 192 muffins and cookies altogether. This gives us the equation:

[tex]M + C = 192 \quad \text{(Equation 1)}[/tex]

Next, we're told that Faith sold [tex]\frac{2}{7}[/tex] of her muffins. Therefore, the number of muffins she sold is:[tex]\frac{2}{7}M[/tex]

The number of muffins left after selling is:
[tex]M - \frac{2}{7}M = \frac{5}{7}M[/tex]

Faith then baked another 24 cookies, so the total number of cookies after baking is:
[tex]C + 24[/tex]

At the end, the problem states she had the same number of muffins and cookies. This gives us another equation:

[tex]\frac{5}{7}M = C + 24 \quad \text{(Equation 2)}[/tex]

Now we have a system of two equations:

[tex]M + C = 192[/tex]
[tex]\frac{5}{7}M = C + 24[/tex]

We can solve this system to find the number of muffins, [tex]M[/tex].

First, solve Equation 1 for [tex]C[/tex]:
[tex]C = 192 - M[/tex]

Substitute [tex]C = 192 - M[/tex] into Equation 2:

[tex]\frac{5}{7}M = 192 - M + 24[/tex]

Now simplify the equation:

[tex]\frac{5}{7}M = 216 - M[/tex]

To eliminate the fraction, multiply through by 7:

[tex]5M = 7(216 - M)[/tex]

Distribute the 7:

[tex]5M = 1512 - 7M[/tex]

Combine [tex]M[/tex] terms by adding [tex]7M[/tex] to both sides:

[tex]12M = 1512[/tex]

Solve for [tex]M[/tex] by dividing both sides by 12:

[tex]M = \frac{1512}{12} = 126[/tex]

Therefore, Faith initially baked 126 muffins.

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Rewritten by : Jeany

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