Answer :
Sure! Let's go through the question step-by-step:
Part a: If Magdalena only makes cakes, we need to figure out how many she can make. Each cake requires 3 eggs. Since she has 60 eggs available, we can calculate the number of cakes she can make by dividing the total number of eggs by the number of eggs needed per cake:
[tex]\[
\text{Number of cakes} = \frac{60 \, \text{eggs}}{3 \, \text{eggs per cake}} = 20 \, \text{cakes}
\][/tex]
Magdalena can make 20 cakes if she only makes cakes.
Part b: If Magdalena only makes cookies, we need to determine how many batches of cookies she can make. Each batch of cookies requires 2 eggs. With 60 eggs available, we calculate the number of batches of cookies by dividing the total number of eggs by the number of eggs needed per batch:
[tex]\[
\text{Number of cookie batches} = \frac{60 \, \text{eggs}}{2 \, \text{eggs per batch}} = 30 \, \text{batches}
\][/tex]
Magdalena can make 30 batches of cookies if she only makes cookies.
Part c: If Magdalena decides to make 6 cakes, we need to find out how many batches of cookies she can still make with the remaining eggs. Making 6 cakes will require:
[tex]\[
6 \, \text{cakes} \times 3 \, \text{eggs per cake} = 18 \, \text{eggs}
\][/tex]
After making 6 cakes, the remaining eggs are:
[tex]\[
60 \, \text{eggs total} - 18 \, \text{eggs for cakes} = 42 \, \text{eggs left}
\][/tex]
Now, using the remaining eggs to make cookies:
[tex]\[
\text{Number of cookie batches} = \frac{42 \, \text{eggs}}{2 \, \text{eggs per batch}} = 21 \, \text{batches}
\][/tex]
Magdalena can make 21 batches of cookies after making 6 cakes.
Part d: We want to write an equation to represent the possible combinations of cakes and cookies Magdalena could make using all 60 eggs. Let [tex]\( c \)[/tex] represent the number of cakes and [tex]\( b \)[/tex] represent the number of batches of cookies.
We know that each cake requires 3 eggs and each cookie batch requires 2 eggs. The total number of eggs used is given by the equation:
[tex]\[
3c + 2b = 60
\][/tex]
This equation shows the relationship between the number of cakes [tex]\( c \)[/tex] and the number of cookie batches [tex]\( b \)[/tex] that use up all of Magdalena's 60 eggs.
Part a: If Magdalena only makes cakes, we need to figure out how many she can make. Each cake requires 3 eggs. Since she has 60 eggs available, we can calculate the number of cakes she can make by dividing the total number of eggs by the number of eggs needed per cake:
[tex]\[
\text{Number of cakes} = \frac{60 \, \text{eggs}}{3 \, \text{eggs per cake}} = 20 \, \text{cakes}
\][/tex]
Magdalena can make 20 cakes if she only makes cakes.
Part b: If Magdalena only makes cookies, we need to determine how many batches of cookies she can make. Each batch of cookies requires 2 eggs. With 60 eggs available, we calculate the number of batches of cookies by dividing the total number of eggs by the number of eggs needed per batch:
[tex]\[
\text{Number of cookie batches} = \frac{60 \, \text{eggs}}{2 \, \text{eggs per batch}} = 30 \, \text{batches}
\][/tex]
Magdalena can make 30 batches of cookies if she only makes cookies.
Part c: If Magdalena decides to make 6 cakes, we need to find out how many batches of cookies she can still make with the remaining eggs. Making 6 cakes will require:
[tex]\[
6 \, \text{cakes} \times 3 \, \text{eggs per cake} = 18 \, \text{eggs}
\][/tex]
After making 6 cakes, the remaining eggs are:
[tex]\[
60 \, \text{eggs total} - 18 \, \text{eggs for cakes} = 42 \, \text{eggs left}
\][/tex]
Now, using the remaining eggs to make cookies:
[tex]\[
\text{Number of cookie batches} = \frac{42 \, \text{eggs}}{2 \, \text{eggs per batch}} = 21 \, \text{batches}
\][/tex]
Magdalena can make 21 batches of cookies after making 6 cakes.
Part d: We want to write an equation to represent the possible combinations of cakes and cookies Magdalena could make using all 60 eggs. Let [tex]\( c \)[/tex] represent the number of cakes and [tex]\( b \)[/tex] represent the number of batches of cookies.
We know that each cake requires 3 eggs and each cookie batch requires 2 eggs. The total number of eggs used is given by the equation:
[tex]\[
3c + 2b = 60
\][/tex]
This equation shows the relationship between the number of cakes [tex]\( c \)[/tex] and the number of cookie batches [tex]\( b \)[/tex] that use up all of Magdalena's 60 eggs.
