Question

Sarah baked 560 apple pies and chicken pies. She sold 60% of the apple pies and 25% of the chicken pies. She sold exactly 1/2 of the pies altogether. How many apple pies did she bake?

Answer 1

Answer:

400 apple pies

Step-by-step explanation:

To solve for the number of apple pies baked by her, let's solve using equations and solving them by substitution method.

$\textcolor{steelblue}{\text{\textcircled{1} Define the variables}}$

Let the number of apple pies and chicken pies baked be a and c pies respectively.

$\textcolor{steelblue}{\text{\textcircled{2} Form equations}}$

Total pies baked= 560

a +c= 560 -----(1)

Total pies sold= ½(560)

$\frac{60}{100} \text{a} \: + \frac{25}{100} \text{b} = 280$

0.6a +0.25b= 280 -----(2)

$\textcolor{steelblue}{\text{\textcircled{3} Solve by substitution}}$

Since we are only interested in the value of a, we should eliminate the term c by making c the subject of equation. This ensures that after substitution, the equation will be in terms of a only.

From (1):

c= 560 -a -----(3)

Substitute (3) into (2):

0.6a +0.25(560 -a)= 280

Expand:

0.6a +140 -0.25a= 280

Simplify:

0.35a +140= 280

0.35a= 280 -140

0.35a= 140

Divide both sides by 0.35:

a= 140 ÷0.35

a= 400

$\textcolor{steelblue}{\text{\textcircled{4} Concluding statement}}$

Thus, she baked 400 apple pies.