You have $30 to spend on picking 25 pounds of two different types of fruit at a farm. The apples cost $1.40 per pound the blueberries cost $.90 per pound and the cherries cost $1.10 per pound. You want prices many pounds of apples as the other two fruits combined.
A.) write a system
B.) solve the system
C.) Supposed there are no restrictions on the money you can spend on fruit. Does the problem still have a unique solution? If not give 3 possible solutions
What do you mean by this?
"You want prices many pounds of apples as the other two fruits combined. "
A.) To write the system of equations, we can use the following variables:
Let x = pounds of apples
Let y = pounds of blueberries
Let z = pounds of cherries
According to the given information, we have the following equations:
1) x + y + z = 25 (Total weight of fruit should be 25 pounds)
2) x = y + z (Price of apples should be equal to the other two fruits combined)
B.) To solve this system of equations, we can use substitution or elimination method.
Using substitution:
From equation 2), we can substitute the value of x in equation 1):
(y + z) + y + z = 25
2y + 2z = 25
y + z = 12.5 (Dividing both sides by 2)
Now, we have a system of two equations and two variables:
1) y + z = 12.5
2) x = y + z
Now, let's solve this system using the substitution method.
From equation 1), we can solve for y:
y = 12.5 - z
Substituting this value of y in equation 2):
x = (12.5 - z) + z
x = 12.5
So, the solution to the system is x = 12.5, y = 12.5 - z, and z can take any value between 0 and 12.5.
C.) When there are no restrictions on the money spent, the problem does not have a unique solution because we can choose any combination of pounds for each fruit as long as the total weight is 25 pounds.
Here are three possible solutions:
1) Apples (12.5 pounds), Blueberries (6 pounds), Cherries (6.5 pounds)
2) Apples (12.5 pounds), Blueberries (7 pounds), Cherries (5.5 pounds)
3) Apples (12.5 pounds), Blueberries (8 pounds), Cherries (4.5 pounds)
In each of these solutions, the price of apples will be equal to the price of both blueberries and cherries.