Answer :
Certainly! Let's break down the problem step by step.
1. Understand the Proportion:
Doreen uses 13 apples for every 2 pies. We want to find out how many apples she will use for 12 pies.
2. Set Up the Proportion:
The given proportion is:
[tex]\[ \frac{13}{2} = \frac{a}{12} \][/tex]
where [tex]\( a \)[/tex] is the number of apples needed for 12 pies.
3. Solve for the Missing Number:
To solve for [tex]\( a \)[/tex], we need to find the equivalent value that maintains the same ratio.
- First, identify the relationship between the pies:
[tex]\[ \frac{12}{2} = 6 \][/tex]
This tells us that 12 pies are 6 times as many as 2 pies.
- Since the ratio must be the same on both sides of the equation, we multiply the number of apples for 2 pies (13 apples) by 6:
[tex]\[ a = 13 \times 6 = 78 \][/tex]
4. Confirm the Proportion:
Recalculate to ensure it fits the original ratio:
[tex]\[ \frac{13}{2} = \frac{78}{12} \][/tex]
Simplifying [tex]\(\frac{78}{12}\)[/tex]:
[tex]\[ \frac{78 \div 6}{12 \div 6} = \frac{13}{2} \][/tex]
The original ratios match.
Thus, Doreen will use 78 apples for baking 12 pies.
Intermediate steps:
- Defined the ratio of apples to pies.
- Set up the proportion equation.
- Solved for the missing value by scaling the ratio appropriately.
- Ensured the proportions match to validate the solution.
1. Understand the Proportion:
Doreen uses 13 apples for every 2 pies. We want to find out how many apples she will use for 12 pies.
2. Set Up the Proportion:
The given proportion is:
[tex]\[ \frac{13}{2} = \frac{a}{12} \][/tex]
where [tex]\( a \)[/tex] is the number of apples needed for 12 pies.
3. Solve for the Missing Number:
To solve for [tex]\( a \)[/tex], we need to find the equivalent value that maintains the same ratio.
- First, identify the relationship between the pies:
[tex]\[ \frac{12}{2} = 6 \][/tex]
This tells us that 12 pies are 6 times as many as 2 pies.
- Since the ratio must be the same on both sides of the equation, we multiply the number of apples for 2 pies (13 apples) by 6:
[tex]\[ a = 13 \times 6 = 78 \][/tex]
4. Confirm the Proportion:
Recalculate to ensure it fits the original ratio:
[tex]\[ \frac{13}{2} = \frac{78}{12} \][/tex]
Simplifying [tex]\(\frac{78}{12}\)[/tex]:
[tex]\[ \frac{78 \div 6}{12 \div 6} = \frac{13}{2} \][/tex]
The original ratios match.
Thus, Doreen will use 78 apples for baking 12 pies.
Intermediate steps:
- Defined the ratio of apples to pies.
- Set up the proportion equation.
- Solved for the missing value by scaling the ratio appropriately.
- Ensured the proportions match to validate the solution.
