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

400 apple pies

Explanation:

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

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)

`(60)/(100) \text{a} \: + (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.