Answer:
5 pounds of the Empire apples, 14 pounds of the Red Delicious apples, and 2 pounds of the Golden Delicious apples.
Step-by-step explanation:
Let's call the Empire apples weight at E, the Red Delicious at R, and the Golden Delicious at G. We know that the total weight must be 21 pounds so:
R + E + G = 21 (<em>equation 1</em>)
The total amount of spent must be $25, and the price given is per pound, so the priced paid is the cost multiplied by the weight:
1.40*E + 1.10*R + 1.30*G = 25 (<em>equation 2</em>)
And the weight of the Red Delicious must be equal to twice of the combined weight of the others:
R = 2*(E + G)
E + G = R/2 (<em>equation 3</em>)
Let's substitute equation 3 in equation 1
R + R/2 = 21
(2R + R)/2 = 21
3R = 42
R = 14 pounds.
So, E + G = 7
G = 7 - E (<em>equation 4</em>)
Let's substitute the result of R and the equation 4 in the equation 2:
1.40*E + 1.10*14 + 1.30*(7 - E) = 25
1.40E + 15.40 + 9.10 - 1.30E = 25
0.10E = 25 - 24.50
0.10E = 0.50
E = 5 pounds
G = 7 - E
G = 7 - 5
G = 2 pounds.
