Write a System of Equations.

Question

You have $30 to spend on picking 24 pounds of different types of fruit. The apples cost $1.40 per pound, blueberries cost $.90 per pound and cherries cost $1.10 per pound. I want twice as many pounds of apples as the other 2 fruits combined.

Answer 1

Let the number of pounds of apples = a

Let the number pounds of blueberries  = b

Let the number of pounds of cherries = c

 

 

a + b + c = 24     ------> total number of pounds

 

1.40a + 0.90b + 1.10c = 30  ---------> total cost of fruits

 

2a = b + c   --------> comparison of pounds

 

Answer 2

Let x = lbs of apples, y = lbs of blueberries and z= lbs of cherries.

 

The first equation is simple x + y + z = 24 since you must have a total of 24 lbs of fruit.

 

The second equation revolves around cost, so we multiply the cost of each fruit by its variable and it should equal $30. 1.40x + 0.90y + 1.10z = 30.00

 

The third equation relates the apples vs the blueberries and cherries.  Since we want twice as many apples as blueberries/cherries, we get x = 2(y + z) or in standard form x - 2y - 2z = 0

 

These three equations, listed together, form your system of equations.