Fuji apples cost $3.00 per pound, and Golden Delicious apples cost $2.00 per pound. A child care center purchases 30 pounds of a combination of the two types of apples for a total of $80.
| | Apples | | |
| :---------- | :--------------- | :----------- | :---- |
| | | | |
| | Pounds | Cost per Pound | Total |
| Fuji | 30-q | 3 | x |
| Golden Delicious | q | 2 | |
| Total | 30 | | 80 |
Answer (1)
Define variables: Let f be the pounds of Fuji apples and g be the pounds of Golden Delicious apples.
Set up equations: f + g = 30 and 3 f + 2 g = 80 .
Solve for f using substitution: f = 20 .
Solve for g : g = 10 . The child care center purchased 20 pounds of Fuji apples and 10 pounds of Golden Delicious apples.
Explanation
Problem Analysis Let's analyze the problem. We are given the cost per pound of two types of apples, the total weight of the apples purchased, and the total cost. We need to find the number of pounds of each type of apple purchased.
Setting up Equations Let f be the number of pounds of Fuji apples and g be the number of pounds of Golden Delicious apples. We can set up a system of two equations with two variables:
f + g = 30 (total weight)
3 f + 2 g = 80 (total cost)
Solving for g We can solve this system of equations using substitution or elimination. Let's use substitution. From the first equation, we can express g in terms of f :
g = 30 − f
Substitution Now, substitute this expression for g into the second equation:
3 f + 2 ( 30 − f ) = 80
Solving for f Simplify and solve for f :
3 f + 60 − 2 f = 80 f = 80 − 60 f = 20
Solving for g Now that we have the value of f , we can find the value of g :
g = 30 − f g = 30 − 20 g = 10
Final Answer So, the child care center purchased 20 pounds of Fuji apples and 10 pounds of Golden Delicious apples.
Examples
Imagine you're planning a fruit salad for a party. You know how much each type of fruit costs and how much you want to spend in total. This problem helps you figure out exactly how many pounds of each fruit to buy so you stay within your budget and have enough for everyone. This kind of problem-solving is useful in many real-life situations, from grocery shopping to managing business expenses.
